Intermediate check to avoid fork (2 moves)
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Sometimes you can capture an opponent's piece, but capturing it comes with a disadvantage, for example if your opponent has other threats, or if the piece which can make the capture is currently pinned. An intermediate check is a move giving check that you play instead, which changes the situation so that you can make the capture later without that disadvantage.
In these levels we are looking at intermediate checks to avoid a fork.
Black just grabbed a pawn on g2 with the knight. The idea is to regain the piece with a fork: 1.Kxg2? 2.Re2+ Kf1 3.Rxc2. However White can win with the intermediate check 1.Bb3+, removing the bishop from the fork with tempo, for example 1...Kf6 2.Kxg2, and White is a piece up.
White is down a piece, but the queen on b6 is en prise. Capturing the queen immediately with 1.Rxb6? would allow the knight fork 1...Nf2+, regaining the queen while still being a piece up. However, by exchanging the knights first, White can regain the material with the intermediate check 1.Nxg6+. Black cannot recapture with the queen, because 1...Qxg6 2.Qd8# would be checkmate. After the pawn recaptures, White can take the queen, because after 1...hxg6 2.Rxb6, the rook on f5 is now guarding f2. Black is then going to capture the rook on f5, and has a rook, a bishop, and a pawn for the queen. The material is approximately even, White has regained the material.
Sometimes the intermediate check can be a sacrifice:
Black just captured a knight on e5 with the queen, relying on a knight fork. After 1.fxe5? Ng4+ 2.Kh3 Nxh6 Black would be a rook up. Instead, Black can sacrifice the queen with the intermediate check 1.Qxf8+!, and regain the material, for example 1...Kxf8 2.fxe5, when the knight fork 2...Ng4+ 3.Kg1 Nxe5 would only regain a pawn. White would then be a pawn up in the endgame.
When you can capture an opponent's piece, don't just grab it. Make sure that your opponent doesn't have any threats. Those threats can exist before your move, or only after your move. If such threats exist, consider an intermediate move or check.