-y^3(2x^2y-4xy^2)=-2x^2y^4+4xy^6

*is this correct.?

No, in the last term, the y should be to the fifth power (3+2)

To verify if the equation is correct, we can simplify both sides of the equation and see if they are equal.

Given equation: -y^3(2x^2y - 4xy^2) = -2x^2y^4 + 4xy^6

First, let's simplify the left side of the equation:

-y^3(2x^2y - 4xy^2) =
-2x^2y^4 + 4xy^6

Simplifying the left side:
Distribute the -y^3 to each term inside the parentheses:

-2x^2y^4 + 4xy^6

Now, let's compare the left side and right side of the equation:

Left side: -2x^2y^4 + 4xy^6
Right side: -2x^2y^4 + 4xy^6

Since the left side and right side are identical, the equation is correct.