Who is "their" when it says, "Their behavoir connected to Fitzgerald's commentary on the American Dream"?

You would need to confirm with your teacher or whomever assigned the original question, but it is most likely referring to Gatsby and Nick.  These are two characters who, despite seemingly having everything and doing what society expected of them, were not fulfilled and did not earn their individual "American Dream" at the end of the novel. 

Gatsby rises from the child of poor farmers in the midwest to a man everyone recognizes in New York City.  He throws extravagant parties and has an excessive amount of money, but none of that is enough to get him what he truly desires. On the surface, that desire seems to be Daisy, but as the novel progresses, the reader realizes that Daisy is more than just a woman to Gatsby: she represents youth and beauty and everything he couldn't have when he was poor. At the end of the novel, he loses Daisy and his life when he's forced to confront the idea that Daisy cannot be everything he needs and wants her to be. He dies still clinging to the idea of Daisy and the false illusion that she loves him.

Nick, the narrator, is different in that he is clearly disillusioned with the idea of the American Dream at the end of the novel. He sees Tom and Daisy for what they are, reckless human beings, and retreats back to the midwest, where morality hasn't loosened so much. He must rethink his American Dream and what it means to be happy altogether, because he isn't willing to give up his humanity to be like Tom and Daisy.