。
She asked me if she could use the phone.
Literal
She [topic-は] phone [object-を] use [may-てよい] [question-か] me [to-に] asked.
~てよいか is a formal variant of ~てもいいか ('may I / is it OK to'). The か makes it an embedded question ('whether it's OK to use'), which becomes the object of 尋ねた ('asked'). 尋ねる is a more formal/written verb for 'ask' than 聞く.