$$ \begin{aligned} x+\frac{2}{3} &= \frac{1}{4}x-1&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12x+12\cdot\frac{2}{3} &= 12 \cdot \frac{1}{4}x-12\cdot1&& \text{cancel out the denominators} \\[1 em]12x+8 &= 3x-12&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 8 }$ to the right} \\[1 em]12x-3x &= -12-8&& \text{simplify left and right hand side} \\[1 em]9x &= -20&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= -\frac{20}{9}&& \\[1 em] \end{aligned} $$

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