To solve for \( x \) in the equation \( 45 = x - 12 \), you need to isolate \( x \). The operation currently affecting \( x \) is subtraction (subtracting 12).
Therefore, the inverse operation needed to solve for \( x \) is Addition.
You would add 12 to both sides of the equation:
\[ 45 + 12 = x \]
This results in:
\[ x = 57 \]
So, the correct response is Addition.