To solve the equation \( x^{12} = 6 \) for \( x \), you should take the twelfth root of both sides of the equation. This can be expressed mathematically as:
\[ x = 6^{1/12} \]
Alternatively, you could write it as:
\[ x = \sqrt[12]{6} \]
Therefore, the operation that should be done to both sides of the equation is taking the twelfth root of both sides.