$$ \begin{aligned} \frac{1}{3}x-8 &= \frac{2}{5}x+6&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15 \cdot \frac{1}{3}x-15\cdot8 &= 15 \cdot \frac{2}{5}x+15\cdot6&& \text{cancel out the denominators} \\[1 em]5x-120 &= 6x+90&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ -120 }$ to the right} \\[1 em]5x-6x &= 90+120&& \text{simplify left and right hand side} \\[1 em]-x &= 210&& \text{switch signs on both sides} \\[1 em]x &= -210&& \\[1 em] \end{aligned} $$

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