For all real numbers $x$ with $- 2 \leq x \leq 2$, the inequality $$- k \leq 2 x ^ { 3 } + 3 x ^ { 2 } - 12 x - 8 \leq k$$ holds. Find the minimum value of the positive number $k$. [3 points]
For all real numbers $x$ with $- 2 \leq x \leq 2$, the inequality
$$- k \leq 2 x ^ { 3 } + 3 x ^ { 2 } - 12 x - 8 \leq k$$
holds. Find the minimum value of the positive number $k$. [3 points]