To solve the equation \( \frac{x}{4} = 12 \) using the inverse operation, we first identify that the operation involved is division by 4. The inverse operation of division is multiplication.
So, we can multiply both sides of the equation by 4:
\[ x = 12 \times 4 \]
Calculating that gives:
\[ x = 48 \]
Thus, the correct response is:
Inverse operation is multiplication; x = 48.