$$\frac{2}{x+2} = \frac{3}{x+6}$$

$$ \begin{aligned} \frac{2}{x+2} &= \frac{3}{x+6}&& \text{multiply ALL terms by } \color{blue}{ (x+2)(x+6) }. \\[1 em](x+2)(x+6)\cdot\frac{2}{x+2} &= (x+2)(x+6)\cdot\frac{3}{x+6}&& \text{cancel out the denominators} \\[1 em]2x+12 &= 3x+6&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]2x-3x &= 6-12&& \text{simplify left and right hand side} \\[1 em]-x &= -6&& \text{switch signs on both sides} \\[1 em]x &= 6&& \\[1 em] \end{aligned} $$

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