$$ \begin{aligned} \frac{2}{5}a+4 &= \frac{5}{6}a+2&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30 \cdot \frac{2}{5}a+30\cdot4 &= 30 \cdot \frac{5}{6}a+30\cdot2&& \text{cancel out the denominators} \\[1 em]12a+120 &= 25a+60&& \text{move the $ \color{blue}{ 25a } $ to the left side and $ \color{blue}{ 120 }$ to the right} \\[1 em]12a-25a &= 60-120&& \text{simplify left and right hand side} \\[1 em]-13a &= -60&& \text{ divide both sides by $ -13 $ } \\[1 em]a &= \frac{-60}{-13}&& \\[1 em]a &= \frac{60}{13}&& \\[1 em] \end{aligned} $$

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