$$ \begin{aligned} 3x+9 &= 4x+6&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ 9 }$ to the right} \\[1 em]3x-4x &= 6-9&& \text{simplify left and right hand side} \\[1 em]-x &= -3&& \text{switch signs on both sides} \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$