If the infinite sequence, M, is defined as M1 = 6, M2 = 96,

I think you mean to write that M_k = 10^k - 4, and not 10k - 4.

When I first read the question, I ask - what even number q would divide every term in the sequence? The only possibilities are 2 and 6, since these are the only even divisors of the first term of the sequence, which is 6. Each other term in the sequence is clearly divisible by 2, and since the digits of each term are multiples of 3, each term will also be divisible by 3, and thus by 6. So the question is really asking if we can determine that q is either 2 or 6.

Statement 1 then is clearly insufficient. From Statement 2, q is an even number which divides at least two terms in the sequence. Certainly q might be 2 or 6, but if you notice that each term in the sequence besides the first term ends in 96, you can see that each term in the sequence besides the first must be a multiple of 4. So q could also be equal to 4, and even combined the two Statements are not sufficient, and the answer is E.