I have manage to split the screen vertically. So far so good. But now i want to resize the ratio of the screen using mouse, that is, using mouse to adjust the divider line, such that it can simultaneously adjust the size at both sides of the split.

I'm not sure mouse-movement of the split line is possible (although it absolutely should be). I just tried and could not seem to figure it out either. You can use the existing controls (number spinners) until someone says how to do it or BF adds the feature if it is missing.

if it can't be done by mouse, can we do it by shortcut ?

Maybe you can create multiple different monitor profiles where the only difference between each is the split configuration. Then in Functions, under the Monitor Configuration section, you'll see all your monitor profiles and you can assign key combinations to load a particular profile. So using this, I can switch between profiles where the screen is split 2x3 or 2x2.

There is no visual indication of the change but you could do something with a different wallpaper under each profile (draw faint split lines to each wallpaper?) Too bad there is no way to assign a different wallpaper for each monitor split.

Alternatively, DisplayFusion also helped me with Functions that lets me expand a window so it fills an adjacent slice. So if I have 2x3 splits and a window in the lower-left, I can press ctrl-alt-right once to make the window expand to the right to include the lower-middle slice. I can run the same combo for the same direction or any other direction to keep expanding that way. Only thing I didn't have time to work out is a function to shrink the window the same way.

Maybe a combination of the two solutions would work? Have a standard profile with your commonly used slice configuration. Then if you want fine adjustment of the window size, switch to a different profile with much more slices (eg: 2x3 -> 20x30). You could even script the resizing function to automatically switch to the other profile just for the duration of the resize.

But this is all really a workaround using what is currently possible. It would be nice if you can just put your mouse over the touching border of two windows and be able to adjust both window edges together. Window's built-in split-screen supports this.