The young woman's question - 'how do we fight an ideology with weapons?' is a good one.
But, first things first, Jihadis fight with weapons, so must the West in response. Our great countries must bomb and shoot Jihadis to death. Wipe them out. Destroy them.
Re the ideology, the West and moderate Muslims must fight against Jihadi ideology. When Jihadists say that infidels must be killed moderate Muslims must speak up about living within Western laws, and put Islamic verses into context.
The majority of Muslims don't commit atrocities but that kinda misses the point. Islam is not a peaceful religion, all you have to do is consider the example of Muhammad. That dude wasn't peaceful, anything but.