The person having the greatest Number of votes for President, shall be the President, if such number be a majority of the whole number of Electors appointed; and if no person have such majority, then from the persons having the highest numbers not exceeding three on the list of those voted for as President, the House of Representatives shall choose immediately, by ballot, the President.

In what way was the Twelfth Amendment important in the election of 1824?

No presidential candidate had received the majority of Electoral College votes.
Some states had illegally appointed their electors to the Electoral College.
The House of Representatives had not yet been elected for that year.
The Speaker of the House was also a presidential candidate at the time.\