First, distribute the negative sign inside the parentheses on the right side of the equation:

(2mn^2 + 4m^2) - (-mn^2 - 4m^2n - 4m^2)

Now, simplify by removing the parentheses and combining like terms:

2mn^2 + 4m^2 + mn^2 + 4m^2n + 4m^2

Combine like terms:

2mn^2 + mn^2 + 4m^2n + 4m^2 + 4m^2

3mn^2 + 4m^2n + 8m^2

Therefore, the simplified expression is 3mn^2 + 4m^2n + 8m^2.