。
She listened to CDs at random.
Literal
She [topic-は] at-random CDs [object-を] listened.
手当たり次第 (てあたりしだい) is a vivid set phrase meaning 'at random' or 'whatever comes to hand' — literally 'in the order that one's hand touches.' It implies grabbing things indiscriminately. ＣＤを聞く (to listen to CDs) uses the basic [media] + を聞く pattern. The phrase adds energy to an otherwise simple action — she wasn't choosing carefully, she was just going through them one after another.