Here's what's going on:
[beautiful math coming... please be patient] $6x - 8xy$ |
Ignore the plus/minus signs of the terms for the moment, and find the greatest common factor of $\,6x\,$ and $\,8xy\,$, which is $\,2x\,$. |
[beautiful math coming... please be patient] $= \overset{\text{gcf}}{\overbrace{(2x)}}(3) - \overset{\text{gcf}}{\overbrace{(2x)}}(4y)$ |
Rename each term as the greatest common factor, times the remaining factors. Eventually, you won't need to write down this intermediate step. |
[beautiful math coming... please be patient] $= (2x)(3 - 4y)$ | Use the distributive law, backwards! |