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