If 453.6 grams of nitroglycerin were to decompose/ detonate completely, how many grams of water would be produced?

Check out this web site:

http://www.ch.ic.ac.uk/rzepa/mim/environmental/html/nitroglyc_text.htm

It says that 4 moles of nitro produce 10 moles of H2O in a spontaneous decomposition reaction.

That and the nitroglycerin formula should lead you to the answer.