How to accept a Greek gift


12.Ne4+ wins the piece back... or I guess I should say just wins a piece because black sacrificed earlier in the game.
The usual followup to the Kg6 idea (which is a good one to know) is Qg4 or Queen to b1-h7 diagonal check. 10.Qd3+ seems to win after 10...f5 11.exf+ Kxf 12.Rf1+ Ke7 13.Qe4+ Kd6 and 14.Rxf8 with 15.Bf4 to win the queen.
Also there's 10.Qg4 and if 10...Nxe5 11.Qg3 Kf6 (the threat of Ne6+ amazingly attacks 4 pieces at once!) but now 12.Rf1+ Ke7 13.Qxe5 mate. 10...f5 11.exf d5 12.Ne6 doesn't help either.
So I think this greek gift sac was very sound.

Yeah...when my opponent plays the superior, Kg6, I usually follow-up myself with Qg4!! as the threat is to win the queen again. I'm not certain why he left the queen on the back-row.

Sometimes the odd Kh6 is the best move... I can't think of an example. This would be good for me to look up...
Vukovic's Art of Attack book has a good section all about the greek gift.