Suppose one of the people is Bob. Amongst the 5 other people, Bob knows at least 3 of them or he doesn't know at least 3 of them. Without loss of generality, suppose he knows three of them. Amongst those 3 people, if two of them know each other, then those two, along with Bob, are three people who know each other and we're done. Otherwise those three people don't know each other and we're done also!