Okay what bothers me here, assuming the position is legal the bishop at h8 was promoted, the rook at h7 came through the h-file after that, so what was Black's last move? It can't be 1...f6xg5 since the white king would have been in check. It can't be 1...Kg6 since the bishop at g8 has nowhere to be promoted and the king would have been in check on the h-file, disallowing the rook from reaching the spot at h7. This can mean three things: the board is reversed, the position is illegal, or it is Black to move.
Otherwise there is a perfectly trivial mate in 4:
1.Bxg7 ~ 2.Kf4 ~ 3.Bf8 ~ 4.Rh6#;