$$ \begin{aligned} 6+3x &= 2x+3&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]3x-2x &= 3-6&& \text{simplify left and right hand side} \\[1 em]x &= -3&& \\[1 em]x &= -3&& \\[1 em] \end{aligned} $$