$$ \begin{aligned} x-\frac{7}{9} &= \frac{x}{6}&& \text{multiply ALL terms by } \color{blue}{ 18 }. \\[1 em]18x-18\cdot\frac{7}{9} &= 18 \cdot \frac{x}{6}&& \text{cancel out the denominators} \\[1 em]18x-14 &= 3x&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ -14 }$ to the right} \\[1 em]18x-3x &= 14&& \text{simplify left side} \\[1 em]15x &= 14&& \text{ divide both sides by $ 15 $ } \\[1 em]x &= \frac{14}{15}&& \\[1 em] \end{aligned} $$

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