White has two resources: a battery on the f-file and a battery on the seventh rank. The mating square for the vertical formation would be f8, which Black guards with his rook, knight, and king; the mating square for the horizontal formation would be g7, at least for starters, which Black guards with his knight and king. Experimenting with his checks leads White to 1. Rxg7+. Black would have to respond by moving his king to h8 or by capturing White’s rook with his knight. So...

(a) If Black plays Kh8, White has a mating pattern of a sort that is standard with two heavy pieces on the seventh rank: 2. Rxh7+, Kg8; 3. Qf7#. Notice how the queen and rook protect each other while providing overpowering pressure against the king.

(b) If Black instead replies to 1. Rxg7+ with NxR, now what? White then would have 2. Qf7+, where the queen draws protection from the rook on f1 and therefore pushes the king into the corner in the same way we saw in the previous position. After Black’s Kh8, White has two attackers trained on f8 against one defender (Black’s rook). Now 3. Qf8+, RxQ; RxR#.

The important point to see from the outset of the position is that if White can get his queen onto f7 it can force the king to h8 and then drop to the back rank to participate in a mating attack there—a useful idea to have in mind anytime you have a rook and queen both aimed at f7 or a comparable square.