"Held out one's hand" is a phrase that conveys an act of offering or greeting. However, there are many synonyms that can be used to describe this action, each with their own unique connotations. For instance, you could say "extended a hand," which denotes a friendly gesture or willingness to help. "Offered a hand" could imply a sense of generosity or assistance. "Reached out a hand" could suggest a more urgent or desperate appeal. Additionally, depending on the context and tone, you could use phrases like "presented a palm," "gestured a handshake," or "beckoned with a hand" to describe the same action. Synonyms allow for more precise and nuanced language, enabling writers to better convey their intended meaning.