To find the difference of the two polynomials \((9x^{2} - 6x + 2)\) and \((x^{2} + 4 - 39)\), we first need to simplify the second polynomial.
\[ x^{2} + 4 - 39 = x^{2} - 35 \]
Now, we can rewrite the expression we want to simplify:
\[ (9x^{2} - 6x + 2) - (x^{2} - 35) \]
Next, distribute the negative sign:
\[ 9x^{2} - 6x + 2 - x^{2} + 35 \]
Now, combine like terms:
\[ (9x^{2} - x^{2}) + (-6x) + (2 + 35) = 8x^{2} - 6x + 37 \]
Thus, the difference of the two polynomials is:
\[ \boxed{8x^{2} - 6x + 37} \]