The position of Black’s king looks knotty, but this shouldn't cause you to overlook the fact that White (despite facing a mate threat from Black) has half of an Arabian mate in place: Black’s king is on the next diagonal square from White’s knight, and the knight is protected; and h6 is sealed off as a flight square by the pawn on g5. If White could get a heavy piece onto g8, he would mate. That doesn’t seem feasible, but perhaps you can make it so; it’s an idea that can motivate your experiments. White has two heavy pieces at hand: his queen and his rook. This is more than he needs to finish the pattern, so the queen can be sacrificed if necessary. What happens if he starts with QxR+? KxQ is the forced response. Since the knight on f6 guards e8 as well as g8, White can now safely play Re8+—forcing Black’s king back to g7, its original square. And now that the rook once on f8 is off the board, White has Rg8#.
Notice the rough similarities between this position and the previous one. White sees the knight-and-king kernel that suggests a possible Arabian mate. One of his own pieces—here, his queen—is in his own way, so he sacrifices it with check. Then he plays another check to push the king back to its original square; then at last comes the completed mate. This idea of pushing and pulling the king, with checks and perhaps with sacrifices, is a useful way to get a heavy piece where you want it while keeping the key elements of the pattern intact.