A nonzero multiple is any multiple that is not zero. For example, the nonzero multiples of 4 would include 4, 8, 12, 16 and so on.
If a question asks for the multiples of a number, most often it is asking for a list of products obtained by multiplying 1, then 2, then 3 (and so on) by the original number. If a question were to ask for the first two nonzero multiples of 2, the answer would be 2 and 4, as zero is specifically excluded because it is not a nonzero multiple. A zero multiple always equals zero, so there is no need to list it.