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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).
1. **First**: Multiply the first terms:
\[
b \cdot 3b = 3b^2
\]
2. **Outer**: Multiply the outer terms:
\[
b \cdot (-6) = -6b
\]
3. **Inner**: Multiply the inner terms:
\[
8 \cdot 3b = 24b
\]
4. **Last**: Multiply the last terms:
\[
8 \cdot (-6) = -48
\]
Now, combine all these results:
\[
3b^2 - 6b + 24b - 48
\]
Combine like terms:
\[
3b^2 + 18b - 48
\]
So, the simplified form of \((b + 8)(3b - 6)\) is:
\[
\boxed{3b^2 + 18b - 48}
\]
Thus, the correct response is **3b² + 18b − 48**.