Let's simplify the expression step by step:
Given expression: \[ -4(7b + 3) + 24b - 8 \]
Step 1: Distribute -4 into the parentheses: \[ -4 \cdot 7b - 4 \cdot 3 = -28b - 12 \]
So now the expression becomes: \[ -28b - 12 + 24b - 8 \]
Step 2: Combine like terms:
- Combine the terms with \(b\): \[ -28b + 24b = -4b \]
- Combine the constant terms: \[ -12 - 8 = -20 \]
Putting it all together, we have: \[ -4b - 20 \]
Thus, the simplified expression is: \[ \boxed{-4b - 20} \]