To multiply the polynomial \( (b+8)(3b-6) \), you can use 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 \(-6b + 24b\):
\[
3b^2 + 18b - 48
\]
So the simplified form of \( (b+8)(3b-6) \) is:
\[
\boxed{3b^2 + 18b - 48}
\]
The correct answer is:
**3b^2 + 18b - 48**.