How would you factor 12x^4y^3+20x^2y^2-24x^2y

so that might look confusing. Its 12x^4 y^3 + 20x^2 y^2 - 24x^2 y. I would like to know how to factor it please.

4x^2 y(3x^2 y^2 + 5y - 6)

There is an x , y , and 4 common in every piece so you can factor it out.

Because the lowest exponent of y is 1 you can only take out y^1
Because the lowest exponent of x is 2 you can only take out x^2
4 is the greatest common factor for 12 , 20 , 24

4x^2 y (3x^2 y^2 + 5y - 6)

Reasoning:
x^2 * x^2 = x^4
y^1 * y^1 = y^2

12x^4 y^3 + 20x^2 y^2 - 24x^2 y
Everything has a y, so
y(12x^4 y^2 + 20x^2 y - 24x^2)
Everything has an x^2, so
yx^2(12x^2 y^2 + 20y - 24)
Everything is a multiple of 4
4yx^2(3x^2 y^2 + 5y - 6)
And that appears to be the end

Solution:

12x^4 y^3 + 20x^2 y^2 - 24x^2 y.

4 x^2 y (3x^2y^2 + 5y - 6)