$$ \begin{aligned} 2-2(y+1) &= 3(y+4)-(y-2)&& \text{simplify left and right hand side} \\[1 em]2-(2y+2) &= 3y+12-(y-2)&& \\[1 em]2-2y-2 &= 3y+12-y+2&& \\[1 em]2-2y-2 &= 2y+14&& \\[1 em]-2y &= 2y+14&& \text{move the $ \color{blue}{ 2y } $ to the left side} \\[1 em]-2y-2y &= 14&& \text{simplify left side} \\[1 em]-4y &= 14&& \text{ divide both sides by $ -4 $ } \\[1 em]y &= -\frac{14}{4}&& \\[1 em]y &= -\frac{7}{2}&& \\[1 em] \end{aligned} $$

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