$$ \begin{aligned} \frac{5}{6}x-4 &= \frac{2}{3}x+5&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{5}{6}x-6\cdot4 &= 6 \cdot \frac{2}{3}x+6\cdot5&& \text{cancel out the denominators} \\[1 em]5x-24 &= 4x+30&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ -24 }$ to the right} \\[1 em]5x-4x &= 30+24&& \text{simplify left and right hand side} \\[1 em]x &= 54&& \\[1 em]x &= 54&& \\[1 em] \end{aligned} $$

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