$$ \begin{aligned} \frac{5}{6}q-\frac{1}{3}q &= \frac{2}{5}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30 \cdot \frac{5}{6}q-30\frac{1}{3}q &= 30\cdot\frac{2}{5}&& \text{cancel out the denominators} \\[1 em]25q-10q &= 12&& \text{simplify left side} \\[1 em]15q &= 12&& \text{ divide both sides by $ 15 $ } \\[1 em]q &= \frac{12}{15}&& \\[1 em]q &= \frac{4}{5}&& \\[1 em] \end{aligned} $$

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