In Fahrenheit 451, what is the symbolic meaning of the line "the men all moved their hands, putting out the fire together?"
Near the end of the book, Montag has discovered the small enclave of people who memorize books to keep them known. They tell him how their movement is spreading, and how they are determined to keep books available; others come to the movement slowly. As they ready themselves to move camp, Montag helps:
The other men helped, and Montag helped, and there, in the wilderness, the men allmoved their hands, putting out the fire together.
(Bradbury, Fahrenheit 451, Google Books)
The symbolism is that Montag has moved beyond his original vocation of fireman (bookburner). Now, he is putting fires out to help keep books safe instead of setting fires to destroy them. This action helps to convince the group that he is trustworthy.
This quote symbolizes the change in Montag from the beginning to the end of the novel. In the beginning of the novel, Montag used to create fires and burn as a living. Now, he is a changed person and sees that what he did was wrong. Now, he helps put the fires out with other people who are like him. He sees that fire is not only for burning, its also for warmth and to bring people together.