What should come in place of both the question marks in the equation ? ? 128 = 162 ?

Answer: Option A

$$\begin{array}{rl}& \text{Let,}\\ & \frac{x}{\sqrt{128}}=\frac{\sqrt{162}}{x}\\ & \text{Then,}\\ & \iff x^2=\sqrt{128\times 162}\\ & \iff x^2=\sqrt{64\times 2\times 18\times 9}\\ & \iff x^2=\sqrt{8^2\times 6^2\times 3^2}\\ & \iff x^2=8\times 6\times 3\\ & \iff x^2=144\\ & \iff x=\sqrt{144}\\ & \iff x=12\end{array}$$