。
She'll handle the difficult problem skillfully.
Literal
She [topic-は] difficult-problem [object-を] [well-うまく] will-handle [probably-だろう].
うまく is the adverbial form of the i-adjective うまい ('skillful, good'). 処理する ('handle, process') is a formal verb common in business and administrative contexts. ~だろう adds the conjecture 'probably,' giving the speaker's evaluative prediction.