Start writing down cases. You know there has to be at least one '0' digit. There can't be 3 or 4 '0' digits because the sum of the digits is 12. But there could be 2 or 1 '0' digits. Handle those two cases separately.
For 2 '0' digits, what could the other digits be? The possibilities are 39,48,75, and 66. There are two types of possibilities here -- when the digits are distinct and when they are not.
For two specific distinct non-zero digits and two zero digits, there are 6 possible numbers (e.g. 3900, 3090, 3009, 9300, 9030, 9003). You can just write them like that to figure out that there are 6, or you can reason that one of the two non-zero digits has to go first and the other has 3 possible positions. 2\*3=6 so there are 6 ways to have a number with two specific distinct non-zero digits and two zero digits.
Anyway, keep going like that. Write down different cases and count the number of ways to form a number in each case.