Statement 1: x=12u, where u is an integer tells us that x is a multiple of 12. This will not be sufficient to find the gcd. x=8y+12, so x is only a multiple of 12 when y is a multiple of 3 (do you see why?) When y=3 x=36, gcd(3,36)=3. When y=6, x=60, gcd(6,60)=6. INSUFFICIENT
Statement 2: y=12z. plugging this in to the expression and simplifying gives us x=12(8z+1). Clearly, then x and y have 12 as a common factor, but we need to see if z and 8z+1 have any common factors. It is impossible that z and 8z+1 would share a common factor. Anything you can factor out of z, you could factor out of 8z, but the +1 is the deal breaker. For example, if z=9, 8z+1=8(9)+1 if you try to factor a 9 out of 8(9)+1 you get 9(8+1/9), which clearly doesn't work. Thus, 12 is the gcd whenever y is a multiple of 12.
Therefore the answer is B
