$$ \begin{aligned} -\frac{2}{3} &= \frac{3}{4}y+3&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]-12\cdot\frac{2}{3} &= 12 \cdot \frac{3}{4}y+12\cdot3&& \text{cancel out the denominators} \\[1 em]-8 &= 9y+36&& \text{ swap the left and right side of the equation } \\[1 em]9y+36 &= -8&& \text{ move 36 to the right } \\[1 em]9y &= -8-36&& \\[1 em]9y &= -44&& \text{ divide both sides by $ 9 $ } \\[1 em]y &= -\frac{44}{9}&& \\[1 em] \end{aligned} $$

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