$$ \begin{aligned} \frac{5}{6}x-1 &= \frac{1}{3}x+7&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{5}{6}x-6\cdot1 &= 6 \cdot \frac{1}{3}x+6\cdot7&& \text{cancel out the denominators} \\[1 em]5x-6 &= 2x+42&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ -6 }$ to the right} \\[1 em]5x-2x &= 42+6&& \text{simplify left and right hand side} \\[1 em]3x &= 48&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= \frac{48}{3}&& \\[1 em]x &= 16&& \\[1 em] \end{aligned} $$

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