The best method to solve a question like this is to take simple values and evaluate the statements.
In this question we are trying to see if n can divide m completely.
Let’s use the data given in statement I alone:
If m = 1 and n = 1, 2m = 2 is definitely a multiple of n=1. In this case, m is a multiple of n.
If m = 1 and n = 2, 2m = 2 is a multiple of n = 2. In this case, m is not a multiple of n.
Enough to say that statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, we have information about n only. Clearly insufficient to answer the question asked. Answer option B can be eliminated.
Combining statements I and II, we can say the following:
From statement II, we can conclude that n = 3, 7, 11, …….
From statement I, 2m is a multiple of 3 or 7 or 11, and so on. Since 2 is not a multiple of any of these numbers, 2m can be a multiple of 3 or 7 or 11 only if m is a multiple of any of these numbers.
Thus, we are able to answer the question with a definite YES.
The correct answer option is C.
Hope this helps!