"Hand around" is a phrase that refers to the act of passing or distributing items among a group of people. There are several synonyms for this phrase, including "circulate," which suggests a circular motion of the item being passed around. "Share," on the other hand, implies a collaborative effort in dividing the item among the group. Another synonym is "disperse," which suggests a wider distribution of the item. "Distribute" is also a similar term, indicating the spreading of the item among individuals. Lastly, "pass on" can be used in situations where the item is being handed over to the next person without delay. Overall, all these terms indicate the act of sharing or distributing something among a group of individuals.