I make it 495...
...an earlier answer identified that there are 11880 different sets of 4 people you can select from your population of 12.
But now you need to determine how many ways these 4 people can be elected to the distinct positions.
For each of the 11880 sets of 4 people you select, you have to make a further determination.
From the 4 people in the set, you can select any of the 4 for president.
For each of those selections, you can select any of the remaining 3 for vice president.
Then, select any of the remaining 2 for treasurer.
So that's 4! (4 * 3 * 2 * 1) ways to arrange a set of 4 people.
So, then, you have to divide your 11880 sets of 4 people by 4! = 24.