$$ \begin{aligned} 9 &= \frac{4}{3}(4x+12)&& \text{simplify right side} \\[1 em]9 &= \frac{16x+48}{3}&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot9 &= 3 \cdot \frac{16x+48}{3}&& \text{cancel out the denominators} \\[1 em]27 &= 16x+48&& \text{ swap the left and right side of the equation } \\[1 em]16x+48 &= 27&& \text{ move 48 to the right } \\[1 em]16x &= 27-48&& \\[1 em]16x &= -21&& \text{ divide both sides by $ 16 $ } \\[1 em]x &= -\frac{21}{16}&& \\[1 em] \end{aligned} $$

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