Originally posted by DarrieThere were a couple notation mistakes. Black's Rf7 should have been Rf8, and Kxg6 should have been Kxh6.
what you are looking for is probably Rd8+ Qxd8 Qe6+ Kh7 Rxh6 gxh6 Qf7#, but I dont see whats wrong or not clear about my answer.
EDIT: okay, after Rf7 black can play Rh7 Rd7 Qxd7 Rxd7, but thats still an easy win for white.
Also, Fritz points out after 1.Qb3+ Kh7 2.Qf7 Qe8! is a more stubborn defense.