Some issues that can happen on one side of your brain affect how you process left/right. In some cases you can't process one or the other, left or right. If you draw a clock with 0-12 all on one side, like where 0-6 or 6-12 ought to be, that tells a lot.
A really salty speech pathologist can figure out all kinds of stuff about your brain by having you draw a clock, even before she sees the x-rays.
Even more if you curse at her and refuse to do it.