How many Black pieces are loose? Two: both knights. There is no way to attack them at the same time, and no way to attack either of them while threatening the king in some way. Those loose pieces nevertheless are tantalizing targets, so White starts digging for ways to attack one of them and something else of value at the same time. The simplest way to do this is by just looking at squares from which the queen can attack either knight, and then seeing what else can be attacked from the same squares: if not a loose piece, then perhaps a piece that can be made loose. White’s queen can attack the g3 knight by moving to b3 or d3. From d3 the queen also would attack the bishop on a6. That piece isn't loose, and anyway it can strike back at d3. Since White has a target, but one that doesn’t work, he looks for an exchange that would improve it: he can play BxB, provoking RxB. Now d3 has been made safe for White queen and Black has a loose piece—the rook—on a6. Qd3 thus attacks two loose pieces and wins the knight.

You also could have found this by just examining every capture of a piece by a piece that you can initiate: imagine 1. BxB, RxB; ask whether that exchange leaves behind any loose pieces; see that the rook would then be loose; look for ways to attack it along with another loose piece; find Qd3. Either way, this problem resembles the earlier ones where White’s queen had a clear path to a square from which it could attack the king, but needed to loosen the other target with a preliminary exchange to create a good double attack. In other words, imagine that the g3 knight in this problem is the Black king, and the rest of the problem then becomes structurally the same as many we saw earlier in this chapter. The implication: if your queen can attack a loose piece and any other piece, start asking whether the other piece can be loosened (or replaced with something loose) as well.