To evaluate the expression \(-2 - 2h\) for \(h = -6\), we first substitute \(-6\) for \(h\):
\[ -2 - 2(-6) \]
Now, calculate the product:
\[ -2 - 2 \times -6 = -2 + 12 \]
Now, simplify the expression:
\[ -2 + 12 = 10 \]
So the final answer is:
\[ \boxed{10} \]