To simplify the expression \((-8x^2 + 2x + 3) - (-6x^2 - x)\), we start by distributing the negative sign across the second expression:
\[ (-8x^2 + 2x + 3) + (6x^2 + x) \]
Now, we can combine like terms:
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Combine the \(x^2\) terms: \[ -8x^2 + 6x^2 = -2x^2 \]
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Combine the \(x\) terms: \[ 2x + x = 3x \]
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The constant term remains the same: \[ 3 \]
Putting it all together, we have:
\[ -2x^2 + 3x + 3 \]
Thus, the final result is:
\[ \boxed{-2x^2 + 3x + 3} \]