Simplify (9x^2 - 6x+ 2) - (x^2 + 4x - 39).

To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), we first distribute the negative sign through the second polynomial:

\[
(9x^2 - 6x + 2) - (x^2 + 4x - 39) = 9x^2 - 6x + 2 - x^2 - 4x + 39
\]

Now, we combine like terms:

1. For the \(x^2\) terms:
\[
9x^2 - x^2 = 8x^2
\]

2. For the \(x\) terms:
\[
-6x - 4x = -10x
\]

3. For the constant terms:
\[
2 + 39 = 41
\]

Now, putting it all together, we have:

\[
8x^2 - 10x + 41
\]

So, the simplified difference of the polynomials is:

\[
\boxed{8x^2 - 10x + 41}
\]