To simplify the expression \((9x^{2}-6x+2) - (x^{2}+4-39)\), we first need to simplify what's inside the second set of parentheses. We have the expression:
\[ x^{2} + 4 - 39 \]
This simplifies to:
\[ x^{2} - 35 \]
Now we can rewrite the entire expression:
\[ (9x^{2} - 6x + 2) - (x^{2} - 35) \]
Now, we distribute the negative sign across the second set of parentheses:
\[ 9x^{2} - 6x + 2 - x^{2} + 35 \]
Next, we combine like terms. First, we combine the \(x^{2}\) terms:
\[ 9x^{2} - x^{2} = 8x^{2} \]
Next, we combine the constant terms:
\[ 2 + 35 = 37 \]
Thus, the expression simplifies to:
\[ 8x^{2} - 6x + 37 \]
Therefore, the final simplified form of the expression is:
\[ \boxed{8x^{2} - 6x + 37} \]