Nice trick and fun to try it, thanks, OP.
An old trick.. There's a variation of this where you use the two hands encode the two numbers involved. Say if one number is 7 then you fold (bend) three fingers on the left hand leaving two raised fingers. The other number you want to multiply, use the right hand, same technique.
Each raised finger counts at 10. (Two raised fingers 20 etc)
The advantage of this version is that you can use all the fingers and the toes to extend the number range. So to calculate 17 x 18 you use 7 raised fingers and for 18 you use 8 raised toes. But note with this scheme every raised digit has a value of 20 (not 10)
There's another interesting technique helping you to do calculations called the "Trachtenberg Speed System of Basic Mathematics. I had the book somewhere, but you should be able to find the pdf freely.
It was developed by a Russian Jewish Engineer Jakow Trachtenberg while he was held at a Nazi concentration camp.