1. **State the problem:** Evaluate $$6. \left( \sqrt[6]{2^{12}} \right)^3$$. 2. **Recall the rules:** The sixth root of a number is the same as raising it to the power of $\frac{1}{6}$. 3. **Rewrite the expression:** $$\left( \sqrt[6]{2^{12}} \right)^3 = \left( 2^{12 \times \frac{1}{6}} \right)^3 = \left( 2^2 \right)^3$$ 4. **Simplify the powers:** $$\left( 2^2 \right)^3 = 2^{2 \times 3} = 2^6$$ 5. **Calculate the final value:** $$2^6 = 64$$ **Final answer:** 64