1. **State the problem:** Solve the quadratic equation $3y^2 - 6y = 0$ for $y$. 2. **Formula and rules:** To solve quadratic equations, we can factorize the expression and use the zero product property which states if $ab=0$, then either $a=0$ or $b=0$. 3. **Factor the equation:** $$3y^2 - 6y = 3y(y - 2) = 0$$ 4. **Apply zero product property:** Set each factor equal to zero: $$3y = 0 \implies y = 0$$ $$y - 2 = 0 \implies y = 2$$ 5. **Final answer:** The solutions to the equation are $y = 0$ and $y = 2$.