$$ \begin{aligned} \frac{32}{5}x-10 &= \frac{22}{5}x+6&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5 \cdot \frac{32}{5}x-5\cdot10 &= 5 \cdot \frac{22}{5}x+5\cdot6&& \text{cancel out the denominators} \\[1 em]32x-50 &= 22x+30&& \text{move the $ \color{blue}{ 22x } $ to the left side and $ \color{blue}{ -50 }$ to the right} \\[1 em]32x-22x &= 30+50&& \text{simplify left and right hand side} \\[1 em]10x &= 80&& \text{ divide both sides by $ 10 $ } \\[1 em]x &= \frac{80}{10}&& \\[1 em]x &= 8&& \\[1 em] \end{aligned} $$

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