The problem asks to multiply the polynomials $(b + 8)(3b - 6)$.

We will use the distributive property (also known as FOIL for binomials) to expand the expression:

1. First term: $b \times 3b = 3b^2$
2. Outer term: $b \times (-6) = -6b$
3. Inner term: $8 \times 3b = 24b$
4. Last term: $8 \times (-6) = -48$

Now combine like terms:

$3b^2 + (-6b + 24b) - 48 = 3b^2 + 18b - 48$

So, the simplified expression is $3b^2 + 18b - 48$.

Looking at the options, the correct answer is the first one: $\boxed{3b^2 + 18b - 48}$

Would you like more details on polynomial multiplication or have any questions? Here are some related questions to explore:

1. How do you apply the distributive property to larger polynomials?
2. Can FOIL be used for polynomials with more than two terms?
3. How do you factor polynomials like the one we just simplified?
4. What happens when the terms in both binomials are negative?
5. How does polynomial division differ from polynomial multiplication?

Tip: Always check for common factors before expanding or simplifying polynomials; sometimes you can factor directly!