$$ \begin{aligned} \frac{2}{3}x+\frac{1}{4}x+9 &= x&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{2}{3}x+12\frac{1}{4}x+12\cdot9 &= 12x&& \text{cancel out the denominators} \\[1 em]8x+3x+108 &= 12x&& \text{simplify left side} \\[1 em]11x+108 &= 12x&& \text{move the $ \color{blue}{ 12x } $ to the left side and $ \color{blue}{ 108 }$ to the right} \\[1 em]11x-12x &= -108&& \text{simplify left side} \\[1 em]-x &= -108&& \text{switch signs on both sides} \\[1 em]x &= 108&& \\[1 em] \end{aligned} $$

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