In the above mentioned November 2011 Watchtower article, in note 17, it says:
According to VAT 4956, this eclipse occurred on the 15th of the third Babylonian month, which suggests that the month of Simanu began 15 days earlier. If the eclipse fell on July 15, 588 B.C.E. according to our Julian calendar, then the first day of Simanu would be June 30/July 1, 588 B.C.E. Therefore, the first Babylonian month (Nisanu) would have started the new year two months earlier, on May 2/3. While normally the year of this eclipse would have begun on April 3/4, VAT 4956 states on line 6 that an extra month (intercalary) was added after the twelfth (last) month (Addaru) of the preceding year. (The tablet reads: “8th of month XII 2 .”) Therefore, this made the new year actually not start until May 2/3. Thus, the date of this eclipse in 588 B.C.E. well fits the data on the tablet.
However, as I was again studying VAT 4956 last night, I found the following:
* Line 16 says, “The 9 th , solstice.”
* In Line 12, we find it is month 3, that is Simanu.
* In Line 17, we find an eclipse on the 15 of month 3.
The Watchtower is saying that the eclipse occurred on July 15, 588 BC under their adjusted calendar. However, taking in Line 16, that would mean that summer solstice was on July 9 th , 588 BC. However, the summer solstice in 588 BC, was on July 29 th . Their calendar is in error.
Of course, VAT 4956 points to 568 BC. The 9 th of the 3 rd month was June 29 th , 568 BC. That would make the 15 th of the 3 rd month, July 4/5.
Forgive me if this has already been brought out. And if there is a flaw in my understanding here, let me know.