$$ \begin{aligned} \frac{6-x}{9} &= \frac{1}{3}&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9 \cdot \frac{6-x}{9} &= 9\cdot\frac{1}{3}&& \text{cancel out the denominators} \\[1 em]6-x &= 3&& \text{ move 6 to the right } \\[1 em]-x &= 3-6&& \\[1 em]-x &= -3&& \text{switch signs on both sides} \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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