Now we move to a slightly higher level of difficulty. These are positions where there is a square from which your queen might attack the enemy king and a loose piece, but where another piece or two blocks the way—blocking the queen’s path to the forking square, or its path from the forking square to one of the targets. Once you see such a situation, the methods for resolving it are straightforward enough; but often it can be hard to see in the first place.
Our first pattern consists of cases where the queen's path to the forking square is blocked. You discover this situation by looking for the ingredients for a double attack and finding a square from which it can be made; then you consider whether the queen’s path to the square can be cleared with a threat or exchange.
In the position to the left, start by looking for the raw elements of a fork. Why, look: with Qa8, White can fork Black's king and his a7 pawn. How splendid! Yet perhaps we can do better. First, does Black have any loose pieces? Yes, the rook at d7. Ideally you want to check his king and attack the rook at the same time. Are there squares from which the queen could do that? Sure: e6 or e8 (in principle d5 and f7 would work, too, but the rook protects those so they aren't worth worrying about—and then there's c8, which is inaccessible). So if the Black bishop on e5 were out of the way, White would have a good double attack. Can the bishop be captured by something other than the queen? No, and anyway after any capture Black would recapture with its pawn (now on f6) and the White queen’s path still would be blocked. You want the e-file cleared, so instead try threatening the bishop with a pawn that it will have to flee. White thus plays f3-f4. If Black moves the bishop out of the way to d6, Qe8+ wins the rook. (In the alternative, of course, Black might choose just to forfeit the bishop; his best reply to f3-f4 is Qh5, allowing him to reply to f4xB with f6xe5.)
The hard part here is seeing the potential for a fork in the first place, since at the outset your queen has no promising checks. The trick is to go with the clues that are available: see the loose piece, and realize there is a square from which you could give check—i.e., a forking square—on e8.