When a piece is attacked and defended several times over, you don't need to calculate every line, you need to count. Count the attackers, count the defenders, and if attackers outnumber defenders, a capture usually wins material. If they don't, it usually loses.
One more rule makes the counting work: capture with your CHEAPEST attacker first. Leading with an expensive piece lets the defender trade up, your rook or queen for their minor piece, and turns a winning count into a losing one.
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Black's d5 pawn is attacked twice (knight and rook) but defended only once (the bishop).
Two attackers, one defender. Start the capture with the cheapest attacker.
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