$$ \begin{aligned} \frac{2}{3}(9x-12)+4x &= -12&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{2}{3}(9x-12)+3\cdot4x &= 3\cdot(-12)&& \text{cancel out the denominators} \\[1 em]18x-24+12x &= -36&& \text{simplify left side} \\[1 em]30x-24 &= -36&& \text{ move -24 to the right } \\[1 em]30x &= -36+24&& \\[1 em]30x &= -12&& \text{ divide both sides by $ 30 $ } \\[1 em]x &= -\frac{12}{30}&& \\[1 em]x &= -\frac{2}{5}&& \\[1 em] \end{aligned} $$

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