Survey the lines on the board and see that Black’s king and queen are aligned. White has nothing usable to create a pin, but his queen almost can get behind Black’s king and impose a skewer; Qg8, however, loses to KxQ. Might he be able to push the king away from g8 a bit? It would have to be done with checks. White’s queen checks, such as Qc7, Qd7, and Qf6, either lose the queen, which White can't afford, or cause Black’s king to leave the diagonal it now shares with his queen, which is no help (or Qe7 pushes the king to the back rank).

How about checks with White’s other piece—his knight? There is one: Ne5+. The knight can't be taken and Black can't interpose anything, so the king must move. Note the squares where the king cannot go: the back rank is forbidden, and e7 and f6 likewise are attacked by White’s queen. (It is important to see invisible constraints of this kind on the king’s movements.) The king legally can move only to e6. This creates room behind it for White to play Qg8+ safely. When the king moves, as it must (though it can’t take the knight, which has protection), White plays QxQ and suddenly has a won game.

Any chance to squeeze in behind the enemy king should be considered carefully, as this is the stuff skewers are made of.