$$2x+3 = \frac{1}{6}\cdot(6+4x)$$

$$ \begin{aligned} 2x+3 &= \frac{1}{6}\cdot(6+4x)&& \text{simplify right side} \\[1 em]2x+3 &= \frac{4x+6}{6}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot2x+6\cdot3 &= 6 \cdot \frac{4x+6}{6}&& \text{cancel out the denominators} \\[1 em]12x+18 &= 4x+6&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ 18 }$ to the right} \\[1 em]12x-4x &= 6-18&& \text{simplify left and right hand side} \\[1 em]8x &= -12&& \text{ divide both sides by $ 8 $ } \\[1 em]x &= -\frac{12}{8}&& \\[1 em]x &= -\frac{3}{2}&& \\[1 em] \end{aligned} $$

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