To determine which expression simplifies to the same expression as \( 4x^2 - 3x^2 + 5x - 24 \), we first simplify the given expression.
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Combine like terms in \( 4x^2 - 3x^2 + 5x - 24 \):
\[ (4x^2 - 3x^2) + 5x - 24 = x^2 + 5x - 24 \]
Now we have the expression \( x^2 + 5x - 24 \).
Next, we will check each of the responses to see if any of them simplify to \( x^2 + 5x - 24 \).
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\( 4x(x - 6) \): \[ 4x(x - 6) = 4x^2 - 24x \] (This does not match.)
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\( (x + 8)(x - 3) \): \[ (x + 8)(x - 3) = x^2 - 3x + 8x - 24 = x^2 + 5x - 24 \] (This matches!)
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\( (x + 6)(x - 4) \): \[ (x + 6)(x - 4) = x^2 - 4x + 6x - 24 = x^2 + 2x - 24 \] (This does not match.)
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\( 2(x - 12) \): \[ 2(x - 12) = 2x - 24 \] (This does not match.)
The only expression that simplifies to \( x^2 + 5x - 24 \) is \( (x + 8)(x - 3) \).
Thus, the correct response is:
\[ \boxed{(x + 8)(x - 3)} \]