An Unexpected Method of Multiplication Is Offered by Arnold from "Hey Arnold!"

An unexpected method of multiplication is offered by Arnold from "Hey Arnold!". The method works for multiplying by 9 and, it would seem, corresponds to an old Chinese rule of multiplying on the fingers:

To obtain the result of multiplying by nine, hold both hands open and fold down the finger whose number corresponds to the number being multiplied; the number of fingers remaining to the left gives the tens in the resulting number, and the number of fingers remaining to the right gives the units.

But how the notation proposed by Arnold actually works, I have not quite understood. If anyone knows, I await an explanation.