Figure[White to move]

White's queen can capture the Black rook or bishop, and his knight could give a fork on d7 if Black's bishop didn't protect the square. But the most important feature of the position is not any of this; it's something considerably harder to see. It is that White’s bishop and e1 rook both are aimed at e8, a square adjacent to Black’s king. Yes, it helps to see pieces so aimed even where obstacles lie in their path; for it may be possible to clear the obstacles away. As a practical matter you see this by going piece by piece and noting that your bishop has a clean attack on e8, which at least is interesting. You look for a way to throw a heavy piece at that square, recognizing the makings of the bishop-and-rook mating pattern we have seen elsewhere. You see that you already have a rook on the e-file, and the question becomes whether the idea can be executed with Re8#. Diagnose the obstacles.

First, White’s knight and Black’s bishop block the rook’s path. Second, Black’s rook on c8 protects the mating square. When you are removing multiple obstacles, the order of moves can be quite important; the first stage of your operations may affect the second. In this case it is clear that White can capture the guard of the mating square with QxR, but if he starts with this move, Black recaptures BxQ—and now there is no way for White to vacate his knight from e5 with a threat that leaves the path to e8 clear (if he plays Nd7+, Black plays BxN and e8 still is guarded). But if you play the reverse move order, the sequence works fine. Nd7+ comes first, requiring Black to play BxN to quash the fork. Notice that the e-file now is clear. Then comes QxR+, removing the guard of e8. Black’s bishop takes White’s queen and is left unable to protect e8. Now Re8 mates for White.

If Black is observant he will see all this coming as soon as White plays the fork Nd7+; so instead of capturing with BxN, he will play Ke7, avoiding mate but forfeiting his queen. The removal of the guard via QxR never quite occurs, but the threat of it forces Black to make terrible concessions.

A simpler way to see this? Just spot the knight fork Nd7+, imagine Black thwarting it with his bishop, ask how the board looks afterwards, and see the e-file opened for the e1 rook to use to drive through to the Black king's position. The rook on c8 and bishop on d7 are in the way, but then White removes them both easily enough with the check QxR.