The detail that best supports Rachel's prediction that Penelope will discover the stranger's true identity is the line "Abroad in the great world, he may have heard rumors about Odysseus—may have known him!" This detail suggests that Penelope believes the stranger may have information or knowledge about Odysseus, her true lord who has been absent for a long time. By calling the stranger to her chamber and wanting to greet and question him, Penelope is actively seeking information that could potentially reveal the stranger's true identity as Odysseus.