To solve the equation \( \frac{x}{4} = 12 \) using the inverse operation, we need to isolate \( x \).
The equation is currently dividing \( x \) by 4. The inverse operation of division is multiplication. Therefore, to isolate \( x \), we will multiply both sides of the equation by 4:
\[ x = 12 \times 4 \]
Calculating the right side:
\[ x = 48 \]
So the correct inverse operation is multiplication.
Thus, the correct answer is:
D. Inverse operation is multiplication; x = 48.