Figure[White to move]

Here is another trickier position. Black has two loose pieces: the rook and the knight. The knight is out of reach, but what about the rook? It almost seems that it could be taken for free by the queen right now; then Black plays QxN, attacking White’s queen, and White has the exchange to show for his trouble. But remain calm and see if you can find something that is better still; don't assume the first good move you find is the best one possible. The queen has no good checks here, but the geometry of Black’s position should be provocative: QxR aims the queen at Black’s king and also attacks the bishop at a5, which would then (i.e., with the rook captured) be left loose. So see if you can move your knight away from e6 with a threat. The first type of threat to consider is a check. Ng5+ is no good, as it gives Black a way to both extinguish the check, save the rook, and guard the targeted piece (the bishop on a5) in one stroke: RxN.

So now consider your other knight check: 1. Nd8+, in reply to which Black has to either take the knight with his queen or else move his king. If he plays 1. …QxN, White has 2. QxR, forking Black’s king and bishop and winning a rook with the sequence. If Black instead moves his king to f8 or g8 in reply to the knight check, the results for him are even worse. If the king goes to g8, it still gets checked by QxR and mate follows soon for White; if Black moves his king instead to f8, then after QxR White can hold off on QxB and instead move his own rook over to the h-file and prepare to drop it to h8, creating havoc there (likely in the form of a skewer).

For now, though, it is enough to have seen the power of the initial move Nd8. The challenge of this problem, a bit like the challenge of the previous one, is that White ends up taking a piece that was not loose at the start by inflicting a check that also was not available at the start. There are various ways you might have spotted the idea: by recognizing the relationship between Black’s bishop and king, which looks like a lot of other double attacks we have seen; or by examining every check from the outset (standard practice), finding Nd8+, and seeing that afterwards QxR wins the bishop; or by seeing that even if the bishop at a5 is not loose, it would become loose as soon as White played QxR with only the white knight standing in the way of a good fork. You look for ways the knight can evacuate its square with check, and there you have it.