I don't have time to deal with this letter. Could you handle it?

Literal

I [topic-は] this letter [object-を] process do time [subject-が] not. You, process do-give [question-かね].

Two sentences in one input. Note 君 ('you'), a casual second-person pronoun typically used by males to peers or subordinates — significantly less polite than あなた but not rude. ~てくれる asks the listener to do something for the speaker; combined with the masculine softener かね (very dated, 'eh? / will you?'), it sounds like an older man addressing a junior. 処理する ('to process, to handle') is a businesslike noun+する verb.