Why did the house of representatives support john quincy adams over andrew jackson?

Adams won against Jackson because of the great influence given by the president of The House Of Representatives Henry Clay.  

Explanation:

In the presidential elections of 1824 Andrew Jackson won more popular votes than John Quincy Adams and that situation was repeated in the Electoral College. However, in this last one no one obtain a majority so that the next step in the selection process was to let The House Of Representatives elect the next president.

In this situation, where Henry Clay was the president of the house, gave his whole support to Adams. He conviced the majority to choose Adams instead of Jackson, who Clay hated the most.  

the answer would be:

b. race