。
Please look after Tanaka-san, okay?
Literal
Tanaka-san [genitive-の] matter [object-を] entrust [assertive-よ].
A short delegation. ~のことを頼む is a set phrase meaning 'please look after X,' 'please take care of X (matter).' こと here is used in a vague all-encompassing sense — 'the matter of X,' 'everything about X.' 頼む ('ask, rely on, entrust') is the core verb. The plain imperative 頼む on its own is masculine-casual for 'I count on you,' 'please [do this].' The よ at the end adds assertive warmth. This is the kind of thing a boss or senior says when handing off responsibility for a colleague's wellbeing.