Throughout the course of the book, Bradbury infuses Montag's hands with a life of their own, almost like they have their own mind. Symbolically speaking, they represent Montag's true desires; they do what he does not have the courage, or even the insight to do yet. For example, he steals a book from Mrs. Blake's house. Montag hasn't fully accepted the fact that he is dying of curiosity about books; he is still in denial. His hands, however, act on that latent desire, and steal the book.
Using Montag's hands goes along with a couple allusions to other stories and quotes. You've probably heard the expression, "with one hand behind my back," to imply that someone is doing something sneaky. Also, there is a phrase that refers to the fact that your right hand doesn't know what your left hand is doing, and also to watch the other hand. Those all refer to the idea that hands have their own minds, and deviously go about conducting mischief. Bradbury plays on that in this book. Montag steals books, or rather, his hands steal books, and seem to know, even before he does, that he wants to take them and read them. His hands foreshadow Montag's own personal journey into discovering the truth.
I hope that those thoughts helped; good luck!
Throughout the novel, Ray Bradbury gives Montag's hands a life of their own. When Montag responds to an alarm at a woman's home, he ends up stealing a book from her library. Montag unconsciously takes the book, and his hands act independently from the rest of his body. Montag realizes that stealing books is against the law, but cannot help himself. Montag's hands symbolically represent his true desires and thirst for knowledge. When Montag grabs the book from Mrs. Blake's home and hides it in his coat, Bradbury writes that Montag's hands had become "infected." Bradbury also personifies Montag's hands by referring to them as "ravenous." Later on in the novel, Faber initially refuses to help Montag, and he begins to rip pages out of the Bible. Again, Bradbury writes that Montag's hands act independently. Faber eventually capitulates and ends up giving Montag a two-way communication device. Montag's hands seem to make the right decisions that lead Montag on his path to enlightenment.