To perform the operation and simplify the expression \((7x^2 - 6x + 2) - (4x - 8) + (-6x^2 + 3x)\), we will start by distributing the negative sign and then combine like terms.
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Rewrite the expression: \[ 7x^2 - 6x + 2 - 4x + 8 - 6x^2 + 3x \]
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Combine like terms:
- For \(x^2\) terms: \[ 7x^2 - 6x^2 = (7 - 6)x^2 = 1x^2 = x^2 \]
- For \(x\) terms: \[ -6x - 4x + 3x = (-6 - 4 + 3)x = -7x \]
- For constant terms: \[ 2 + 8 = 10 \]
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Putting it all together: Now we combine the simplified terms: \[ x^2 - 7x + 10 \]
Thus, the final simplified expression is: \[ \boxed{x^2 - 7x + 10} \]