The simplest understanding of this would be annihilation, but I believe in other threads you have supported the orthodox idea that Gehenna involves eternal suffering or torment. Can you supply any references from ancient sources that the destruction of the wicked was not simply their annihilation?
The verb apolesai "to destroy, become lost, ruined, to perish" in this verse has a wide range of meaning, largely inconsistent with the idea of "annihilation". It is used in Matthew 8:25 in connection with the disciples about to be drowned in the sea, the rupturing and ruining of wine skins in Matthew 9:17, the "lost" sheep of Israel in Matthew 10:6, 15:24, "losing" a reward in Matthew 10:42, and so forth. The sense of "becoming lost" is definitely in view in Matthew 10:39 which occurs a few verses later and which similarly concerns a psukhé "soul, life" becoming apolesas "lost, destroyed":
"Anyone who finds (heurón) his life (tén psukhén autou) will lose (apolesei) it; anyone who loses (apolesas) his life (tén psukhén autou) for my sake will find (heurései) it" (Matthew 10:39; cf. 16:25)
The antithesis involving "finding" clearly indicates that "losing" is the corresponding sense. Moreover, apolesai occurs elsewhere with soma "body" and "Gehenna" in Matthew 5:29-30:
"If your right eye should cause you to sin, tear it out and throw (bale) it away; for it will do you less harm to lose (apolétai) one part of you than to have your whole body (holon to soma sou) thrown (bléthé) into Gehenna. And if your right hand should cause you to sin, cut it off and throw (bale) it away; for it will do you less harm to lose (apolétai) one part of you than to have your whole body (holon to soma sou) go to Gehenna" (Matthew 5:29-30).
Here the sense is not of body parts being utterly annihilated but being "thrown away"; the analogy is that a person who goes to Gehenna is "thrown away" there like refuse. The saying here is also paralleled by Matthew 18:9: "And if your eye causes you to sin, gouge it out and throw (bale) it away. It is better for you to enter life (zóén eiselthein) with one eye than to have two eyes and be thrown (bléthénai) into the fire of Gehenna (tén Géennan tou puros)". The sense of apolesai thus seems to have more of a sense of "perish by becoming lost" than "become annihilated".
Moreover, other references to eschatological judgment in Matthew are not consistent with annihilation. Matthew 13:42, 50 says that the wicked are "thrown (balousin) into the furnace of fire (kaminon tou puros), where there will be weeping (klauthmos) and gnashing (brugmos) of teeth". There wording here is very similar to Matthew 5:29-30 and 18:9 (i.e. balousin/bale + eis kaminon/Geennan tou puros), indicating we are dealing with the same eschatological conception, and the people thrown into this fiery furance are said to experience "weeping" and "gnashing" of teeth over their fate. This emotive reflection on one's loss of "life" directly conflicts with the Society's annihilationist persepctive. Similar references to such emoting occur in Matthew 8:12, 22:13, 24:51, 25:30. Finally, the reference to "eternal fire" in Matthew 18:8 corresponds to the "eternal fire" that the wicked (the "goats") are sent into in Matthew 25:41, and a few verses later they are said to "go away into eternal punishment (eis kolasin aiónion) but the righteous to eternal life (zóén aiónion)" (v. 46). Eschatological punishment in apocalyptic literature of the period, particularly involving fire, usually assume some conscious experience of torment (e.g. "he will be tormented (basanisthésetai) with burning sulphur...the smoke of their torment (basanismou) rises forever and ever," Revelation 14:10-11; cf. ebléthé eis ten limnén tou puros "thrown into the lake of fire" and basanisthésontai hémeras kai nuktos "they will be tormented day and night forever" in 20:10).
Other similar texts of the period include:
"This accursed valley [i.e. Gehenna] is for those who are accursed forever. Here will be gathered all the accursed, who utter with their mouth an improper word against the Lord and speak hard things against his glory. Here they will be gathered, and here will be their habitation at the last times, in the days of righteous judgment in the presence of the righteous for all time. Here the godless will bless the Lord of glory, the King of eternity" (1 Enoch 27:2-3).
"Woe to you, unrighteous, when you afflict the righteous on a day of hard anguish, and burn them in fire, for you will be recompensed according to your deeds ... in the heat of a blazing fire you will burn... Know that down to Sheol they will lead your souls; and there they will be in great distress, and in darkness and in a snare and in a flaming fire. Into great judgment your souls will enter, and the great judgment will be for all generations of eternity. Woe to you, you will have no peace" (1 Enoch 100:7-9, 103:7-8).
"They showed me there a very frightful place; and all kinds of torture and torment are in that place, cruel darkness and lightless gloom. And there is no light there, and a black fire blazes up perpetually, with a river of fire that comes out over the whole place, fire here, freezing ice there, and it dries up and it freezes, and very cruel places of detention and dark and merciless angels, carrying instruments of atrocities torturing without pity. And I said, 'Woe, woe! How very frightful this place is!' And those men said to me, 'This place, Enoch, has been prepared for those who do not glorify God, who practice on the earth the sin which is against nature ... divinations, trafficking with demons, who boast about their evil deeds' " (2 Enoch 10:1-4).
"It is for this reason that Cain was handed over by God for seven punishments, for in every hundredth year the Lord brought upon him one plague. When he was two hundred years old suffering began and in his nine hundredth year he was deprived of life. For he was condemned on account of Abel his brother as a result of all his evil deeds, but Lamech was condemned by seventy times seven. Until eternity those who are like Cain in their moral corruption and hatred of brother shall be punished with a similar judgment" (Testament of Benjamin 7:3-5).
"There shall no more be Beliar's spirit of error, because he will be thrown into eternal fire. And those who died in sorrow shall be raised in joy; and those who died in poverty for the Lord's sake shall be wakened to life ... the impious shall mourn and the sinners shall weep, but all peoples shall glorify the Lord forever" (Testament of Judah 25:3-5).
"In the same way the body is connected to the soul and the soul to the body, to convict them of their common deeds. And the judgment becomes final for both body and soul, for the works they have done whether good or evil" (Apocryphon of Ezekiel 2:10-11).
"If you have any means of torture, apply it to my body, for my soul you cannot touch even if you would...Let us with all our hearts consecrate ourselves to God, who gave us our lives, and let us use our bodies as a bulwark for the Law. Let us not fear him who thinks he is killing us, for great is the struggle of the soul and the danger of eternal torment lying before those who transgress the commandment of God. Therefore let us put on the full armor of self-control, which is divine reason. For if we so die, Abraham and Isaac and Jacob will welcome us, and all the fathers will praise us" (4 Maccabees 10:4, 13:13-17)
"The Pharisees ... believe that every soul is immortal, but that only the souls of the virtuous pass on into another body, while those of the wicked are punished with an everlasting vengeance" (Josephus, Jewish War 2.163).
"They believe that souls have immortal power, and that there are rewards and punishments under the earth for those who have done well or badly in their life. Evil souls receive eternal imprisonment, while virtuous ones have an easy route to a new life" (Josephus, Antiquities 18.14).
"Then the heavenly one will give souls and breath and voice to the dead and bones fastened with all kinds of joinings, flesh, and sinews. Bodies of humans, made solid in heavenly manner, breathing and set in motion, will be raised on a single day. Then Uriel, the great angel, will break the gigantic bolts of unyielding and unbreakable steel, of the gates of Hades, not forged of metal; he will throw them open wide and will lead all the mournful forms to judgment ... these he will gather and set at the tribunal of God. When Sabaoth Adonai, who thunders on high, dissolves fate and raises the dead, he takes his seat on a heavenly throne ... Moses, the great friend of the Most High will come, having put on flesh. Great Abraham himself will come, Isaac and Jacob, Joshua, Daniel and Elijah... And then all will pass through the blazing river and the unquenchable flame. All the righteous will be saved, but the impious will then be destroyed for all ages... These and the sorcerers and sorceresses in addition to them will the anger of the heavenly imperishable God also bring near to the pillar, around which an undying fiery river flows in a circle. All these at once the angels of the immortal, everlasting God will punish terribly from above with whips of flame, having bound them around with fiery chains and unbreakable bonds. Then, in the dead of night, they will be thrown under many terrible infernal beasts in Gehenna, where there is immeasurable darkness. But when they have inflicted many punishments on all whose heart is evil, then later a fiery wheel from the great river will press them hard all around, because they were concerned with wicked deeds. Then they will wail here and there at a distance in most piteous fate, fathers and infant children, mothers and weeping children at the breast. They will not have their fill of tears, nor will their voice be heard as they lament piteously here and there, but in distress they will shout at length below dark, dank Tartarus. In places unholy they will repay threefold what evil deed they committed, burning in much fire. They will all gnash their teeth, wasting away with thirst and raging violence. They will call death fair, and it will evade them. No longer will death or night give these rest" (Sibylline Oracle 2:221-230, 235-239, 245-247, 252-255, 283-308).
"God himself will again fashion the bones and ashes of men and he will raise up mortals again as they were before. And then there will be a judgment over which God himself will preside, judging the world again. And many as sinned by impiety, these will a mound of earth cover, and broad Tartarus and the repulsive recesses of Gehenna. But as many as are pious, they will live on earth again when God gives spirit and life and favor to these pious ones" (Sybilline Oracle 4:172-92).
"For the earth will surely give back the dead at that time ... then my judgment will be strong, and those things which have been spoken of before will come. And it will happen after this day which he appointed is over that ... the shape of those who now act wickedly will be made more evil than it is now so that they shall suffer torment ... into startling visions and horrible shapes; and they will waste away even more. For they will first see and then they will go away to be tormented.... [while] the righteous will be changed into any shape which they wished, from beauty to loveliness, and from light to the splendor of glory. For the extents of Paradise will be spread out for them" (2 Baruch 50:2, 4, 51:1-11).
"And the earth shall give up those who are asleep in it; and the chambers shall give up the souls which have been committed to them. And the Most High shall be revealed upon the seat of judgment, and compassion shall pass away, and patience shall be withdrawn, but judgment alone shall remain, truth shall stand, and faithfulness shall grow strong.... Then the pit of torment shall appear, and opposite it shall be the place of rest; and the furnace of Gehenna shall be disclosed, and opposite it the Paradise of delight. Then the Most High will say to the nations that have been raised from the dead, 'Look on this side and on that, here are delight and rest, and there are fire and torments!' " (4 Ezra 7:32-38).
"I saw a soul which five thousand angels punished and guarded. They took it to the East and they brought it to the West. They beat it and they gave it a hundred lashes for each one daily...And after I arose I said, 'Who is this whom they are punishing?' He said to me, 'This is a soul which was found in its lawlessness.' " (Apocalypse of Zephaniah II.1-6).
"These are the servants of all creation who come to the souls of ungodly men and bring them and leave them in this place. They spend three days going around with them in the air before they bring them out and cast them into their eternal punishment...I saw the sea which I had seen at the bottom of Hades. Its waves came up to the clouds. I saw all the souls sinking in it. I saw some whose hands were bound to their neck, with their hands and feet being fettered. I said, 'Who are these?' He said to me, 'These are the ones who were bribed and they were given gold and silver until the souls of men were led astray.' And I saw others covered with mats of fire....All the righteous came running, praying to the Lord Almighty daily on behalf of these who are in all these torments" (Apocalypse of Zephaniah 4:6-7, 10:3-6, 11:6).
Compare with Tertullian:
"When this age reaches its full end, God will sit as judge and his worshippers he will repay with life eternal, and the profane he will condemn to fire as perpetual and unceasing; for the dead, every man of them from the beginning, shall be raised, refashioned and reviewed, that their deserts of either kind, good or evil, may be adjudged" (Tertullian, Apologeticus 18.3-4).