Shut up and do as you're told!

Literal

Be-silent-[and-て] say-[thing-こと] [object-を] listen-[command-け]!

言うことを聞く is the set idiom for 'to obey / do as one is told' — literally 'to listen to what is said.' Combined with the bare imperative 聞け ('listen!') and the adverbial 黙って ('quietly'), the sentence is a sharp, scolding order. Note that there's no overt subject for either 言う or 聞く: who's speaking and who should listen are entirely contextual.