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A capture in chess by a pawn works completely differently from that by any other piece.

It may happen in one of $2$ circumstances.

Normal Pawn Capture

If one of the $2$ diagonally adjacent squares towards the opposing player is occupied by an opposing piece, the pawn may move into that square and capture that piece.

En Passant Pawn Capture

Let pawn $a$ be on the player's $5$th rank.

Let pawn $b$ be of the opposite colour to pawn $a$.

Let pawn $b$ be on its starting position, on one of the files adjacent to the one occupied by pawn $a$.

Let pawn $b$ move forward $2$ spaces, in the process crossing over one of the squares which is under attack from pawn $a$.

Then pawn $a$, on its next move only, may move into that square crossed over by pawn $b$, and capture pawn $b$ "while it is passing".

This mode of capture is known as capture en passant.