To simplify the expression \(-4(7b + 3) + 24b - 8\), follow these steps:
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Distribute \(-4\) to the terms inside the parentheses: \[ -4(7b) - 4(3) = -28b - 12 \]
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Rewrite the expression with the distributed terms: \[ -28b - 12 + 24b - 8 \]
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Combine like terms:
- For the \(b\) terms: \[ -28b + 24b = -4b \]
- For the constant terms: \[ -12 - 8 = -20 \]
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Combine the results: \[ -4b - 20 \]
Thus, the simplified expression is: \[ \boxed{-4b - 20} \]