To evaluate the expression \(-6h^2\) for \(h = -2\), we first substitute \(-2\) for \(h\):
\[ -6(-2)^2 \]
Next, we calculate \((-2)^2\):
\[ (-2)^2 = 4 \]
Now substitute this value back into the expression:
\[ -6 \cdot 4 \]
Now, perform the multiplication:
\[ -6 \cdot 4 = -24 \]
Therefore, the value of the expression \(-6h^2\) when \(h = -2\) is:
\[ \boxed{-24} \]