Let's simplify the expression step by step.
The given expression is: \[ -4(-6 + 9b^2) + -4b^2 + -7 \]
First, we can distribute \(-4\) to the terms inside the parentheses: \[ -4 \cdot -6 + -4 \cdot 9b^2 = 24 - 36b^2 \]
Now, substitute this back into the original expression: \[ 24 - 36b^2 + -4b^2 + -7 \]
Next, we combine like terms. The \(b^2\) terms can be combined: \[ -36b^2 - 4b^2 = -40b^2 \]
Now, combine the constant terms: \[ 24 - 7 = 17 \]
Putting it all together, we have: \[ 17 - 40b^2 \]
Thus, the simplified expression is: \[ \boxed{17 - 40b^2} \]