Before gen 4, Pinsir can learn neither quick attack nor close combat. In gens 4 to 7, both of these moves are egg moves.
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/ds4 bug group,quick attack,close combat
Pinsir
/ds5 bug group,quick attack,close combat
Pinsir
/ds6 bug group,quick attack,close combat
Pinsir
/ds7 bug group,quick attack,close combat
Pinsir
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In gens 4 to 5, this means there are no compatible fathers that can know quick attack and close combat and pass both of those moves to a Pinsir, so Pinsir can't know both of those moves in gens 4 to 5. Starting in gen 6, mothers can pass egg moves, so you can breed a female Pinsir and a compatible father with quick attack (like Scyther), hatch a female Pinsir with quick attack, and breed that with a compatible father with close combat (like Heracross), and hatch Pinsirs with both moves.
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In gen 8, close combat is a TR move, so you can hatch a quick attack Pinsir and teach close combat to it.