The 76385-304LF is an 8-position, 2-row, 2.54mm pitch through-hole header from the Amphenol ICC (FCI) Dubox series.
The closest peer is the 76385-303LF, also an 8-position Dubox header. Gold carries a higher mating cycle rating — if the connector is cycled more than a few dozen times in the field, the gold version is the right call. The 76385-306LF is a 12-position version of the same header — same pitch, same locking, same plating. If the BOM needs more circuits, that's the drop-in with two extra positions per row.
Mates with a Dubox receptacle housing (female) that accepts the matching crimp terminal. The 2-wall shroud on the header side guides the receptacle straight on. Termination is solder — the through-hole pins (0.134" post length) go into the PCB and are wave-soldered. The 2.54mm pitch gives enough room for a standard soldering iron tip or wave solder nozzle.