She held out her hand.

Literal

She [topic-は] hand [object-を] extended.

手を差し出す (to hold out one's hand, to extend one's hand) is a set phrase for offering a handshake, presenting something, or reaching toward someone. 差し出す is a compound verb: 差す (to extend/reach) + 出す (to put out). The gesture implies offering or initiating contact.