$$ \begin{aligned} \frac{x+4}{6}-\frac{1}{3} &= \frac{x}{5}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30 \cdot \frac{x+4}{6}-30\cdot\frac{1}{3} &= 30 \cdot \frac{x}{5}&& \text{cancel out the denominators} \\[1 em]5x+20-10 &= 6x&& \text{simplify left side} \\[1 em]5x+10 &= 6x&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ 10 }$ to the right} \\[1 em]5x-6x &= -10&& \text{simplify left side} \\[1 em]-x &= -10&& \text{switch signs on both sides} \\[1 em]x &= 10&& \\[1 em] \end{aligned} $$

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