$$ \begin{aligned} \frac{x}{2}+\frac{x}{6} &= \frac{x}{4}+1&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{x}{2}+12\frac{x}{6} &= 12 \cdot \frac{x}{4}+12\cdot1&& \text{cancel out the denominators} \\[1 em]6x+2x &= 3x+12&& \text{simplify left side} \\[1 em]8x &= 3x+12&& \text{move the $ \color{blue}{ 3x } $ to the left side} \\[1 em]8x-3x &= 12&& \text{simplify left side} \\[1 em]5x &= 12&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{12}{5}&& \\[1 em] \end{aligned} $$

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