Question

Capt. Beatty says the beauty of fire is that it “destroys responsibility and consequences. A problem gets too burdensome, then into the furnace with it.” Explain how this line is an element of foreshadowing.

Answer 1

This line is foreshadowing because it implies that anything -- even people -- that becomes a burden can easily be destroyed.

Later, when Beatty himself becomes a problem, Montag burns Beatty to death. When Montag killed Beatty, he destroyed the responsibility he owed him. In this way, this line is an element of foreshadowing.

Answer 2

This line foreshadows Captain Beatty's death. Beatty becomes Montag's biggest problem when he makes Montag burn his home and his books. Montag then gets rid of his problem by burning Beatty. 
If you've read to the end of the book, this line can also foreshadow the elimination of the society in which Montag used to live when his city is bombed.