What is an example of a man vs. man conflict in Fahrenheit 451?

Montag vs. Captain Beatty is an example of a man vs. man conflict.

The man versus man conflict, or character versus character, is a conflict between two people.  In literature, this means that two characters are struggling, or one character is struggling with another.  Montag’s main enemy or conflict is his boss at the firehouse, Captain Beatty.

Captain Beatty is an unusual man.  He is supposed to be against books, and yet he can quote widely from literature and history.  He also seems to enjoy baiting Montag and watching him struggle in his own crisis of faith with books.  Beatty knows exactly what is going on with Montag, and seems to relish in torturing him.

When Montag steals the book and finds himself unable to face Captain Beatty and the others, he calls in sick.  Beatty knows immediately what has happened, and comes to let Montag know he knows.  He doesn’t tell Montag he knows he stole a book. He gives him a lecture on the history of firemen.

"Every fireman, sooner or later, hits this. They only need understanding, to know how the wheels run. Need to know the history of our profession. They don't feed it to rookies like they used to. Damn shame." Puff. "Only fire chiefs remember it now." Puff. "I'll let you in on it." (Part I)

Later, when Montag returns to work, Faber has a radio in his ear so that he can guide him through his interactions with Captain Beatty.  Beatty is a worthy adversary.  Montag is no match for him in cunning.  He realizes something else and finds the radio.  He notices Montag listening and hits it out of his ear. Beatty switched the green bullet off and thrust it in his pocket.

"Well--so there's more here than I thought. I saw you tilt your head, listening. First I thought you had a Seashell. But when you turned clever later, I wondered. We'll trace this and drop it on your friend." (Part III) 

Montag does not want to let Beatty get Faber.  He hardly realizes it himself when he switches on the flamethrower and turns it on Beatty. In his last moments, Beatty is shocked.  He did not know Montag had it in him.  In this way, Montag settles his conflict with Beatty- permanently.  He has to go on the run after that.

The conflict between Beatty and Montag represents the conflict in society.  When people can't have books or the firemen come and burn the house down, you have an oppressive society.  Beatty represents that oppression for Montag, and he fights it and eventually wins.