Holding out one's hand is a common gesture in human interaction. It is often used as a form of greeting or handshake and it can symbolize trust or friendship. However, there are many ways to express this gesture without using the exact phrase "holding out one's hand." Some synonyms for this action may include "extending a hand," "offering a hand," or "proffering a hand." Other ways to describe this gesture could include "reaching out one's arm," "presenting one's palm," or "making a gesture of welcome." These various synonyms can add variety and nuance to written or spoken communication, depending on the specific context and tone required.