I can’t do this assignment for you, but I’m happy to provide you with some main ideas to help get you started! The “Allegory of the Cave” is an extended metaphor of sorts that helps Plato illustrate his theory of the forms and argue that it is only with an application of philosophical reasoning that humans can begin to access truth.
The cave that the prisoners are trapped in represents the superficial material world that human beings are born into. The prisoners assume that the shadows that they see on the walls of the cave are real because they are all they have ever seen. But then when one of the prisoners leaves the cave and sees the sun, he realizes that the prisoners inside the cave are wrong about what is real.
Plato explains the purpose of the allegory when he says that:
if you interpret the upward journey and the study of things above as the upward journey of the soul to the intelligible realm, you’ll grasp what I hope to convey.
He is explaining that a human’s journey towards the realm of higher truth is similar to the experience of the prisoner learning about the sun when he left the cave. Much like that prisoner, Plato is saying that when we study philosophy (“the study of things above”) we begin to understand that what we see around us is but mere superficial imitations of the unchanging perfect forms in the higher realm. This point the root of his theory of forms, also called the theory of ideas, and he is thus trying to articulate it in this Allegory.