There are several synonyms for the phrase "hand out" including distribute, give out, dispense, issue, provide, offer, and share. These terms all refer to the act of giving something to someone else. Distribute implies that something is being given out to a group of people, while give out suggests that something is being given to individuals. Dispense is a more formal term that is often used in medical or legal contexts. Issue is a term commonly used in official or bureaucratic settings. Provide and offer both suggest a level of assistance or generosity, while share implies that something is being divided or passed on between multiple parties.