To simplify the product \((3b + 9)(8b - 4)\) using the distributive property, we will apply the distributive property (also known as the FOIL method for binomials) to every term in the first parenthesis with every term in the second parenthesis.
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Multiply \(3b\) by \(8b\): \[ 3b \cdot 8b = 24b^2 \]
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Multiply \(3b\) by \(-4\): \[ 3b \cdot (-4) = -12b \]
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Multiply \(9\) by \(8b\): \[ 9 \cdot 8b = 72b \]
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Multiply \(9\) by \(-4\): \[ 9 \cdot (-4) = -36 \]
Now, combine all these results: \[ 24b^2 - 12b + 72b - 36 \]
Next, combine the like terms: \[ -12b + 72b = 60b \]
So, the expression simplifies to: \[ 24b^2 + 60b - 36 \]
Therefore, the final simplified expression is: \[ \boxed{24b^2 + 60b - 36} \]
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