3y^2+8=0

(3y+2)+(3y-2)=8+0
3y=-8
y=3/8
Radical and Rational Exponent
this chapter is hard for me.

No, it is wrong.

3y^2=-8
y^2=-8/3

Now you can't to anymore in the real number system, as there is no such thing as a square root of a negative number. But if you define i as sqrt (-1), then
y=+- sqrt (8/3) * i