Help White Escape Mate!
13. Ne3 also prevent mate on g2, although it doesn't attack the queen on h3 and make black move it back. Then if 13... Bc5 white can just leave it there, since after 14... Bxe3 15. fxe3, g2 is covered too.
cmh0114, black can't take on f4, since the pawn is pinned (taking on f4 would put his own king in check)
If it's hard, just analyze it a little more. If it's easy, congratulations, I hope your escaping skills are just as good in an actual game.
It's not that hard, you can do it!