You can write the combination formula which is in the picture. Now if you can't guess what the varibles mean I'll tell you. N is the amount of digits you're allowed to use, and k is the amount of spots allowed in a number. Plus if the factorial sign or ! isn't part of your common knowledge, it means to multiply all below it stopping at 1. Finally if you comput your information into the formula you find out that there's 24 combinations. I hope this answers your question.
Since the four digit number cannot start with a 0, it has to start with a 2. So we are left with determining the number of ways to fill the rest 3 digits using only 0's or 2's. 2xxx.
For the third digit position, there are 2 choices (0 or 2) , for each of these, there are 2 choices at the second digit, and for each such choice there are 2 possible choices for the first digit. The total of possibilities is 2*2*2=2^3=8.
Interestingly, this is the same number of possibilities encoded in 3 bits in the binary system.
