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To multiply the polynomial \((b + 8)(3b - 6)\), we can apply the distributive property (also known as the FOIL method for binomials):
1. Multiply the first terms:
\(b \cdot 3b = 3b^2\)
2. Multiply the outer terms:
\(b \cdot (-6) = -6b\)
3. Multiply the inner terms:
\(8 \cdot 3b = 24b\)
4. Multiply the last terms:
\(8 \cdot (-6) = -48\)
Now combine all these results:
\[
3b^2 - 6b + 24b - 48
\]
Combine the like terms:
\[
3b^2 + (24b - 6b) - 48 = 3b^2 + 18b - 48
\]
Thus, the result of multiplying \((b + 8)(3b - 6)\) simplifies to:
\[
\boxed{3b^2 + 18b - 48}
\]