Final answer:
The best supporting quotation for how Northup is entrapped by his hopes for the future, provided by Brown and Hamilton, is the one stating the large advantages and flattering representations made to him, leading him to accept their offer.
Step-by-step explanation:
The quotation that best develops the idea that Hamilton and Brown use Northup's hopes for his future to entrap him is: "So largely did they describe the advantages that would result to me, and such were the flattering representations they made, that I finally concluded to accept the offer." (paragraph 4). This passage illustrates how Northup is convinced by Hamilton and Brown through their persuasive and flattering inducements to follow them, which ultimately leads to his entrapment. The description of the benefits and the bright future they promise prey on Northup's aspirations, which is a cunning tactic to entrap him. By choosing to accompany them based on these hopes, Northup falls into their trap.