To solve the equation \( x^{12} = 6 \) for \( x \), you should take the 12th root of both sides. This can be done by raising both sides of the equation to the power of \( \frac{1}{12} \):
\[ x = 6^{\frac{1}{12}} \]
So, the correct action to take is to raise both sides to the power of \( \frac{1}{12} \).