To solve this equation, I need to get rid of the absolute value signs. One way to do that is to consider the different cases when $y$ is positive, zero, or negative. If $y>0$, then the equation becomes $y=2(y-1)$, which simplifies to $y=2y-2$. Subtracting $y$ from both sides, I get $0=y-2$, or $y=2$. So one solution is $y=2$. If $y=0$, then the equation becomes $0=2(0-1)$, which simplifies to $0=-2$. This is not true, so $y=0$ is not a solution. If $y<0$, then the equation becomes $-y=2(-y-1)$, which simplifies to $-y=-2y-2$. Adding $y$ to both sides, I get $0=-y-2$, or $y=-2$. So another solution is $y=-2$. These are the only two solutions, since I covered all the possible cases. The product of the solutions is $y_1y_2=2(-2)=-4$. 
Find the product of the solutions of: $|y|=2(|y|-1)$.