Can you help clarify this article on polytonality?

http://www.pbs.org/brubeck/theMusic/polyrhythmPolytonality.htm

The part " for example, re-harmonized it by putting the left hand in the original key (often the root and a note a 10th higher than the root in the left hand) and then playing chords with his right hand in a key a sixth higher than the root of the left hand."

Would that mean you would play a chord on the sixth degree of your key, which would still be in your original key, or would that mean you would build chords off of the 6th of your original key?