To simplify \( 4x^2 - 3x^2 + 5x - 24 \), we can first combine the like terms:
\[
4x^2 - 3x^2 = (4 - 3)x^2 = 1x^2 = x^2
\]
So, we can rewrite the expression as:
\[
x^2 + 5x - 24
\]
Next, we will factor the quadratic expression \( x^2 + 5x - 24 \).
We need to find two numbers that multiply to \(-24\) (the constant term) and add to \(5\) (the coefficient of the linear term). The numbers \(8\) and \(-3\) satisfy this:
\[
8 + (-3) = 5 \quad \text{and} \quad 8 \times (-3) = -24
\]
So, we can factor the quadratic as:
\[
(x + 8)(x - 3)
\]
Now, we can compare this factorization with the options given:
1. \(2(x - 12)\)
2. \(4x(x - 6)\)
3. \((x + 6)(x - 4)\)
4. \((x + 8)(x - 3)\)
The correct option that simplifies to the same expression as \(4x^2 - 3x^2 + 5x - 24\) is:
\[
\boxed{(x + 8)(x - 3)}
\]