。
Please, just be quiet.
Literal
I-ask-[because-から] quietly do [emphasis-よ].
頼むから ('please, I'm begging you,' literally 'because I'm asking you') is an emphatic plea opener. 静かにしてよ uses ~にする ('make [something] X') with the na-adjective 静か ('quiet') in adverbial form — '[make it] quiet.' The terminal よ adds insistence. Classic exhausted-parent or annoyed-roommate energy.