。
She raised her hand to ask a question.
Literal
She [topic-は] question [object-を] do [purpose-ために] hand [object-を] raised.
~ために (in order to) states the purpose of raising her hand — to ask a question. 質問をする (to ask a question) uses the standard [noun + をする] pattern. 手を上げた (raised her hand) is the familiar classroom gesture. The purpose construction ために is slightly more formal than the purpose に (verb stem + に + motion verb).