$$ \begin{aligned} 23x-\frac{2}{9} &= \frac{12}{6}&& \text{multiply ALL terms by } \color{blue}{ 18 }. \\[1 em]18\cdot23x-18\cdot\frac{2}{9} &= 18\cdot\frac{12}{6}&& \text{cancel out the denominators} \\[1 em]414x-4 &= 36&& \text{ move -4 to the right } \\[1 em]414x &= 36+4&& \\[1 em]414x &= 40&& \text{ divide both sides by $ 414 $ } \\[1 em]x &= \frac{40}{414}&& \\[1 em]x &= \frac{20}{207}&& \\[1 em] \end{aligned} $$

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