$$ \begin{aligned} \frac{2}{3}x-4 &= \frac{5}{6}x+1&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{2}{3}x-6\cdot4 &= 6 \cdot \frac{5}{6}x+6\cdot1&& \text{cancel out the denominators} \\[1 em]4x-24 &= 5x+6&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ -24 }$ to the right} \\[1 em]4x-5x &= 6+24&& \text{simplify left and right hand side} \\[1 em]-x &= 30&& \text{switch signs on both sides} \\[1 em]x &= -30&& \\[1 em] \end{aligned} $$

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