To simplify the expression \((9x^2 - 6x + 2) - (x^2 - 4x - 39)\), we start by distributing the negative sign to the terms in the second parentheses:
\[ 9x^2 - 6x + 2 - x^2 + 4x + 39 \]
Now we combine like terms. First, we combine the \(x^2\) terms:
\[ 9x^2 - x^2 = 8x^2 \]
Next, we combine the \(x\) terms:
\[ -6x + 4x = -2x \]
Finally, we combine the constant terms:
\[ 2 + 39 = 41 \]
Putting it all together, we get:
\[ 8x^2 - 2x + 41 \]
Thus, the simplified expression is:
\[ \boxed{8x^2 - 2x + 41} \]