Verified answer

It doesn't factor out any further than this:

-12xy^3+9x^4y-6x^3y

To factor, you pull out common terms to the front, outside the parenthesis.

-6x^3y + 9x^2y^2 - 12xy^3

=> first step, find LCD which is -3xy so it becomes: -3xy(2x^2-3xy+4y^2)

=> then because 2x is squared you can factor out that as well so: -3xy(2x+y)(x-4y)