To determine which of the given expressions simplifies to the same expression as \( 4x^2 - 3x^2 + 5x - 24 \), we first simplify the original expression:
\[
4x^2 - 3x^2 + 5x - 24 = (4x^2 - 3x^2) + 5x - 24 = 1x^2 + 5x - 24 = x^2 + 5x - 24
\]
Now, we need to check which of the provided options simplifies to \( x^2 + 5x - 24 \).
1. **Option 1: \( 4x(x-6) \)**
\[
4x(x - 6) = 4x^2 - 24x
\]
2. **Option 2: \( (x+6)(x-4) \)**
\[
(x + 6)(x - 4) = x^2 - 4x + 6x - 24 = x^2 + 2x - 24
\]
3. **Option 3: \( (x+8)(x-3) \)**
\[
(x + 8)(x - 3) = x^2 - 3x + 8x - 24 = x^2 + 5x - 24
\]
4. **Option 4: \( 2(x - 12) \)**
\[
2(x - 12) = 2x - 24
\]
From this simplification, we can see that **Option 3: \( (x + 8)(x - 3) \)** simplifies to \( x^2 + 5x - 24 \), which matches the expression we simplified from the original statement.
So, the correct answer is: **(x + 8)(x - 3)**.