What does Faber give Montag at the end of their conversation?why?
I assume you are talking about their conversation at Faber's house, not the one in the park. And I'm assuming you are talking about the first conversation at Faber's house. If so, Faber gives Montag the "bullet."
The "bullet" is a two way communicator. With it, Faber can talk to Montag (the bullet will be in Montag's ear) and Faber can hear what Montag is saying.
Faber is giving this to Montag so that Faber can help him out. This way, he can give Montag advice on what to do in certain situations. Specifically, he wants to tell Montag what to say to Beatty.
Faber gives Montag a "green bullet" at the end of their conversation in Fahrenheit 451. It enables Faber to hear Montag and anyone around him, and enables Faber to talk to Montag.
Faber explains that this is his role in changing the society. He believes himself to be cowardly. He is not able to go out and be on the "front lines," so to speak. He says that he can only stay safe at home, and let Montag go out and be at risk. This device enables him to direct Montag from the safety of his home.