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To multiply the polynomial \((b + 8)(3b - 6)\), we can use the distributive property (also known as the FOIL method for binomials):
\[
(b + 8)(3b - 6) = b \cdot 3b + b \cdot (-6) + 8 \cdot 3b + 8 \cdot (-6)
\]
Now, calculate each term:
1. \(b \cdot 3b = 3b^2\)
2. \(b \cdot (-6) = -6b\)
3. \(8 \cdot 3b = 24b\)
4. \(8 \cdot (-6) = -48\)
Combine these results:
\[
3b^2 - 6b + 24b - 48
\]
Now combine like terms:
\[
3b^2 + (24b - 6b) - 48 = 3b^2 + 18b - 48
\]
So, the simplified result is:
\[
\boxed{3b^2 + 18b - 48}
\]