To simplify the expression 3x^n - 2(x^n+2) + y^n+2(3x^n-2 - y^n-2), we can start by distributing the coefficients:

3x^n - 2(x^n+2) + y^n+2(3x^n-2) - y^n+2(-2)

Next, we can simplify the exponents:

3x^n - 2x^n+2 + y^n+2(3x^n-2) - y^n+2(-2)

Now, let's simplify the terms with the same base:

3x^n - 2x^n * x^2 + y^n+2(3x^n-2) - y^n+2(-2)

Simplifying further:

3x^n - 2x^n+2 + 3x^n+y^n+2 - 2y^n+2

Finally, we can combine like terms:

(3x^n + 3x^n) - 2x^n+2 + (y^n+2 - 2y^n+2)

Simplifying:

6x^n - 2x^n+2 + (y^n+2 - 2y^n+2)

So, the simplified expression is 6x^n - 2x^n+2 + (y^n+2 - 2y^n+2).