How many 4 number combinations can be made from 1234?

4! (factorial) or 24.

If you break it down, the first position can have the numbers 1 through 4 (4 possibilities), the second has one less by being second (3 possibilities), the third has two less (2) and the last one is just 1. Multiply each position by the next (4*3*2*1) and you get 24.

* * * * *

That is totally incorrect. The given answer refers to the number of PERMUTATIONS not the number of COMBINATIONS.

The combination 1234 is the same as 1243, 2134 etc. In fact, all 4 permutations are the same combination. Consequently there is only 1 combination.