$$\frac{6}{5}x+12 = 2x+3$$

$$ \begin{aligned} \frac{6}{5}x+12 &= 2x+3&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5 \cdot \frac{6}{5}x+5\cdot12 &= 5\cdot2x+5\cdot3&& \text{cancel out the denominators} \\[1 em]6x+60 &= 10x+15&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ 60 }$ to the right} \\[1 em]6x-10x &= 15-60&& \text{simplify left and right hand side} \\[1 em]-4x &= -45&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= \frac{-45}{-4}&& \\[1 em]x &= \frac{45}{4}&& \\[1 em] \end{aligned} $$

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