Could you answer the phone for me?

Literal

I [of-の] place-of [phone-を] take-for-me [question-ませんか].

かわりに ('in place of, instead of') marks the speaker's substitute role. 電話を取る ('to answer the phone') is a set phrase — literally 'take the phone.' 取ってくれませんか is the standard polite request. A common domestic/office scenario.