...right or left hemisphere?
If you see the dancer spin clockwise you are using the left side of your brain and if it's the opposite it's your right hemisphere... It's not a joke BTW and you can even consciously decide to change the spinning direction.
The figure IS spinning counter-clockwise. I can make myself see the illusion that she is spinning clockwise if I wish, but analysis of the shadow points out that it is, in fact, illusory.
And the whole "right brain/left brain" bit has been discredited for a long long time.