$$ \begin{aligned} \frac{1}{2}+\frac{6}{x} &= \frac{5}{6}&& \text{multiply ALL terms by } \color{blue}{ 2x\cdot6 }. \\[1 em]2x\cdot6\cdot\frac{1}{2}+2x\cdot6\cdot\frac{6}{x} &= 2x\cdot6\cdot\frac{5}{6}&& \text{cancel out the denominators} \\[1 em]6x+72 &= 10x&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ 72 }$ to the right} \\[1 em]6x-10x &= -72&& \text{simplify left side} \\[1 em]-4x &= -72&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= \frac{-72}{-4}&& \\[1 em]x &= 18&& \\[1 em] \end{aligned} $$

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