To solve $(4x^2y^3 + 2xy^2 - 2y) - (-7x^2y^3 + 6xy^2 - 2y)$, we will first distribute the negative sign through the second set of parentheses, and then combine like terms.

First, distribute the negative sign: $4x^2y^3 + 2xy^2 - 2y - (-7x^2y^3 + 6xy^2 - 2y)$ $= 4x^2y^3 + 2xy^2 - 2y + 7x^2y^3 - 6xy^2 + 2y$

Now, combine like terms:

1. Combine the $x^2y^3$ terms: $4x^2y^3 + 7x^2y^3 = 11x^2y^3$

2. Combine the $xy^2$ terms: $2xy^2 - 6xy^2 = -4xy^2$

3. Combine the $y$ terms: $-2y + 2y = 0$

Thus, the resulting expression is: $11x^2y^3 - 4xy^2$

The coefficients for $x^2y^3$, $xy^2$, and $y$ are $11$, $-4$, and $0$ respectively.

If you have any questions or need further details, please let me know.

Here are 5 more questions you might find interesting:

1. Simplify the expression $(3a^2b + 2ab^2 - 4b) - (5a^2b - ab^2 + 3b)$.
2. Factor the polynomial $x^3 - 3x^2 + 2x$.
3. Solve the quadratic equation $2x^2 - 5x + 3 = 0$.
4. Find the derivative of $f(x) = x^4 - 2x^3 + x - 5$.
5. Evaluate the integral $\int (3x^2 - 2x + 1) dx$.

Tip: When combining like terms, always ensure that you correctly align the terms with the same variables and powers to avoid mistakes.