Given that t is divisible by 12 and we need to find what is the least possible integer value of a for which $\frac{t^2}{2^a}$ might not be an integer

t is divisible by 12 => t is a multiple of 12 => t = 12x where x is an integer

$\frac{t^2}{2^a}$ = $\frac{(12x)^2}{2^a}$ = $\frac{(2^2*3*x)^2}{2^a}$ = $\frac{2^4*3^2*x^2}{2^a}$

Now, in numerator 2 has a power of 4. So, a should be more than 4 for $\frac{t^2}{2^a}$ to not be an integer
=> a = 5

So, Answer will be D.
Hope it helps!