$$2 \cdot \frac{x}{3}-\frac{1}{4} = \frac{x}{6}+\frac{3}{2}$$

$$ \begin{aligned} 2 \cdot \frac{x}{3}-\frac{1}{4} &= \frac{x}{6}+\frac{3}{2}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12\cdot2 \cdot \frac{x}{3}-12\cdot\frac{1}{4} &= 12 \cdot \frac{x}{6}+12\cdot\frac{3}{2}&& \text{cancel out the denominators} \\[1 em]8x-3 &= 2x+18&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ -3 }$ to the right} \\[1 em]8x-2x &= 18+3&& \text{simplify left and right hand side} \\[1 em]6x &= 21&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= \frac{21}{6}&& \\[1 em]x &= \frac{7}{2}&& \\[1 em] \end{aligned} $$

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