$$ \begin{aligned} -4x-6 &= -3x-8&& \text{move the $ \color{blue}{ -3x } $ to the left side and $ \color{blue}{ -6 }$ to the right} \\[1 em]-4x+3x &= -8+6&& \text{simplify left and right hand side} \\[1 em]-x &= -2&& \text{switch signs on both sides} \\[1 em]x &= 2&& \\[1 em] \end{aligned} $$