To simplify the given expression:

$\frac{8x - 24}{4x - 12}$

We can start by factoring out common factors from both the numerator and the denominator.

1. In the numerator, factor out 8: $8x - 24 = 8(x - 3)$

2. In the denominator, factor out 4: $4x - 12 = 4(x - 3)$

Now the expression becomes: $\frac{8(x - 3)}{4(x - 3)}$

Since $(x - 3)$ appears in both the numerator and the denominator, we can cancel it out (assuming $x \neq 3$).

Thus, the simplified expression is: $\frac{8}{4} = 2$

So, the correct answer is 2.

Let me know if you need further clarification or if you have more questions!

Here are some related questions to expand the topic:

1. How do you simplify rational expressions with different powers of $x$?
2. What would happen if $x = 3$ in the expression $\frac{8x - 24}{4x - 12}$?
3. Can we simplify rational expressions that do not have common factors?
4. How do you factor quadratic expressions in the numerator and denominator?
5. What are the restrictions when simplifying rational expressions?

Tip: When simplifying rational expressions, always check for common factors first, and be sure to account for any restrictions (values that make the denominator zero).