To simplify the denominator of the expression \( 4 + (-6) \cdot 2 / -(-3)^2 \), we first focus on the expression within the denominator, which is:
\[ -(-3)^2 \]
First, we calculate \( (-3)^2 \):
\[ (-3)^2 = 9 \]
Next, we apply the negative sign in front of it:
\[ -(-3)^2 = -9 \]
Thus, the denominator simplifies to \(-9\).
Therefore, the simplified denominator is \(-9\).