Simplify: 2x^3y^2+ 4x^2z / 2x^4

The way you typed it ....

= 2x^3 y^2 + 2z/x^2

If you meant: (2x^3y^2+ 4x^2z) / (2x^4)
then
= y^2 /x + z/x^2
= (x y^2 + z)/x^2