Figure[White to move]

You see the battery on the d-file almost ready to mate with Qd8 then Rd8, but not quite because Black’s king guards d8 along with his rook. When you see this pattern—the enemy king at the edge of its pawn cover, and so able to defend the mating square you need—consider whether the king can be driven back behind its pawn cover with a check along the diagonal. A first thought for White might be to use the queen with a move like Qd7; this would work if d7 weren’t guarded by Black’s queen, but it is. Still, consider all the resources you can use to achieve your goals. Or consider every check. Either way you find 1. Bh3+, requiring Black to play Kb8. Now comes 2. Qd8+, RxQ; 3. RxR#.