Take statement 1)- since x is divisible by 8, x is multiple of 8. the values can be 8,16,... if x=8, then 96 (=2^5 * 3) is divisible by x. but if x is any number other than 8 (say 40= 8*5), then 96 is not divisible. so we cannot tell if 96 is divisible by x with the help of statement 1. so cross out A and D. we are left with options B,C and E.
Take statement 2)- since x is divisible by 12, x is multiple of 12. the values can be 12,24,... if x=12, then 96 (=2^5 * 3) is divisible by x. but if x is any number other than 12 (say 36=12*3), then 96 is not divisible. so we cannot tell if 96 is divisible by x with the help of statement 2. Cross out B. we are left with options C and E.
If we take both statements 1 and 2 together, then x is divisible by both 8 and 12, ie x is a multiple of 24 (LCM of 8 and 12). the values can be 24,48,96,..but for any values of x above 96, say 120, 96 is not divisible by x.

So the correct answer is E.

Hi,
As irock has rightly posted,
From(1) : If x = 16, 96 is divisible by x
If x = 40, 96 is not divisible by x
Not sufficient
From(2) : If x = 24, 96 is divisible by x
If x = 36, 96 is not divisible by x
Not sufficient
Combining (1) & (2), If x = 24, 96 is divisible by x
If x = 72, 96 is not divisible by x
Not sufficient

Hence, answer E