White’s queen is en prise to the knight on c6, but of course we avoid reflexive resort to defensive play. Look for an attack; study the enemy king and its vulnerabilities. The long diagonal leading to Black’s king is open; this is an opportunity that must be inspected closely. White has control over the diagonal with his queen, and his dark squared bishop is available as well. (This also was true in the previous problem. It is important to notice when you have more firepower than you need for such a purpose, as that means you can sacrifice some of it.) White would mate if he were able to move his knight to e7 safely, but the square is defended. So he plays with another knight check: 1. Nf6+. It forces the king to h8 or g7. Now when White moves the knight he will discover check. Black has no loose pieces that would make good targets for the knight, but still: keep looking for mate. Here that means putting the knight where it can stay involved by attacking Black’s weak dark squares. White thus plays 2. Ng4+. Doesn’t this allow Black to extinguish the check with NxQ? Yes, but now White has 3. Bf6+ (protected against KxB by the knight now on g4). The king is forced back to g8, and then White plays 4. Nh6#.

The knight’s three moves here are worth some study; they illustrate the comfort with the piece you want to attain. Indeed, notice that the whole mate is built with bishop and knight moves. The queen, which looks like the dominant piece at the beginning, never moves and serves just to deliver a discovered check before White lets it get taken.

Incidentally, another way the sequence can go is 1. Nf6+, Kh8; 2. Ng4+, f7-f6; 3. Bxf6+, RxB; 4. QxR#. The bishop on c4 seals off g8 as a flight square; for by the end of the sequence the knight on d5 and the pawn on f7 both are out of the way.