The prospects for mate here aren't obvious. But when you have two bishops ready to attack, as White does, be mindful of patterns that take advantage of them. The first two checks to try should come naturally: 1. Rh3+, using the open file and forcing the king to g8; then 2. Be6+, aiming one of the bishops into the king’s position from a safe square and forcing it to f8. Okay, but now what? Think about the position the king then would have: its back would be against the wall on the e-file, and the e6 bishop would cut off the light squares around it. It’s a setup for Boden’s mate, coming at the king along the dark diagonal leading from h6. The idea is obscured by the pawn on g7, but by now you know what to do about it: 3. Qxf6+, g7xQ; and then 4. Bh6#.