The term 'HELLENIC HANGOUT' is a combination of two words: 'HELLENIC, ' which refers to the ancient Greek culture, and 'HANGOUT, ' which is a place where people gather to socialize. The crossword solution for this term is 'Agora, ' which was an open-air marketplace in ancient Greece where people would gather to buy and sell goods, as well as to socialize and discuss politics. Agoras were the center of public life in ancient Greece, and they served as a meeting place for citizens to come together and exchange ideas.