Question

find the possible value or values of y in the quadratic equation z^2 - 4z+ 4 =0

Answer 1

Didn't you mean "Find the possible value or values of z?  y is not at all present in this equation.

z^2 - 4z + 4 = 0 can be factored into (z-2)(z-2).  Thus, the given equation has two equal, real solutions:  z=2 and z=-2.