。
Do what you're asked right away.
Literal
Asked thing [topic-は] right-away do.
頼まれた is the passive of 頼む ('be asked / be requested'). 頼まれた事 = 'things that have been asked of [you]' — a passive relative clause modifying 事. やる is the casual everyday 'to do,' a synonym for する with slightly more colloquial flavor.