$$ \begin{aligned} \frac{10}{9} &= \frac{1}{2}b\cdot\frac{4}{3}&& \text{multiply ALL terms by } \color{blue}{ 18 }. \\[1 em]18\cdot\frac{10}{9} &= 18 \cdot \frac{1}{2}b\cdot\frac{4}{3}&& \text{cancel out the denominators} \\[1 em]20 &= 12b&& \text{ swap the left and right side of the equation } \\[1 em]12b &= 20&& \text{ divide both sides by $ 12 $ } \\[1 em]b &= \frac{20}{12}&& \\[1 em]b &= \frac{5}{3}&& \\[1 em] \end{aligned} $$

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