The problem requires determining the simplified expression that represents the area of a rectangle. The area of a rectangle is found by multiplying the length by the width. Here, the length is $9x^2 + 6x - 3$ and the width is $2x - 8$.

Steps to Simplify:

1. Multiply the two polynomials: $(9x^2 + 6x - 3) \cdot (2x - 8)$

2. Apply the distributive property: $= (9x^2 \cdot 2x) + (9x^2 \cdot -8) + (6x \cdot 2x) + (6x \cdot -8) + (-3 \cdot 2x) + (-3 \cdot -8)$

3. Simplify each term: $= 18x^3 - 72x^2 + 12x^2 - 48x - 6x + 24$

4. Combine like terms: $= 18x^3 - 60x^2 - 54x + 24$

Final Simplified Expression:

$18x^3 - 60x^2 - 54x + 24$

Let me know if you have questions about any steps! Here are some follow-up questions to deepen understanding:

1. What is the significance of combining like terms in polynomial expressions?
2. How can the distributive property be visualized geometrically in this problem?
3. What are some strategies for ensuring no terms are missed when multiplying polynomials?
4. How would the expression change if the width was instead $2x + 8$?
5. Can you factorize the resulting polynomial further? Why or why not?

Tip: When working with polynomial multiplication, aligning like terms systematically helps avoid errors!