$$ \begin{aligned} 2 \cdot \frac{x}{3} &= 3 \cdot \frac{x}{8}+\frac{7}{12}&& \text{multiply ALL terms by } \color{blue}{ 24 }. \\[1 em]24\cdot2 \cdot \frac{x}{3} &= 24\cdot3 \cdot \frac{x}{8}+24\cdot\frac{7}{12}&& \text{cancel out the denominators} \\[1 em]16x &= 9x+14&& \text{move the $ \color{blue}{ 9x } $ to the left side} \\[1 em]16x-9x &= 14&& \text{simplify left side} \\[1 em]7x &= 14&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= \frac{14}{7}&& \\[1 em]x &= 2&& \\[1 em] \end{aligned} $$

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