What number must be added to the expression 16a2 - 12a to make a perfect square ?

Answer: Option A

$$\begin{array}{rl}& {\left(a-b\right)}^2=a^2+b^2+2ab\\ & 16a^2-\text{12}a\\ & =(4a{)}^2-2\times 4a\times \frac{3}{2}+{\left(\frac{3}{2}\right)}^2\\ & \text{Number be added}\\ & \text{ = }{\left(\frac{3}{2}\right)}^2\\ & =\frac{9}{4}\end{array}$$