To simplify the expression, we follow the order of operations and distribute the -4 to the terms inside the parentheses:
-4(7b + 3) + 24b - 8 = -28b - 12 + 24b - 8
Next, we combine like terms:
-28b + 24b - 12 - 8 = -4b - 20
Thus, the simplified expression is -4b - 20.