$$2 \cdot \frac{x}{4x+4} = \frac{6x-12}{4x+4}$$

$$ \begin{aligned} 2 \cdot \frac{x}{4x+4} &= \frac{6x-12}{4x+4}&& \text{multiply ALL terms by } \color{blue}{ 4x+4 }. \\[1 em](4x+4)\cdot2 \cdot \frac{x}{4x+4} &= (4x+4)\frac{6x-12}{4x+4}&& \text{cancel out the denominators} \\[1 em]2x &= 6x-12&& \text{move the $ \color{blue}{ 6x } $ to the left side} \\[1 em]2x-6x &= -12&& \text{simplify left side} \\[1 em]-4x &= -12&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= \frac{-12}{-4}&& \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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