$$ \begin{aligned} \frac{2}{3}x-\frac{1}{4} &= \frac{7}{9}+\frac{x}{12}&& \text{multiply ALL terms by } \color{blue}{ 36 }. \\[1 em]36 \cdot \frac{2}{3}x-36\cdot\frac{1}{4} &= 36\cdot\frac{7}{9}+36\frac{x}{12}&& \text{cancel out the denominators} \\[1 em]24x-9 &= 28+3x&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ -9 }$ to the right} \\[1 em]24x-3x &= 28+9&& \text{simplify left and right hand side} \\[1 em]21x &= 37&& \text{ divide both sides by $ 21 $ } \\[1 em]x &= \frac{37}{21}&& \\[1 em] \end{aligned} $$

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