I wish I'd been taught that as a child instead of the conventional method. I had no end of trouble with subtraction because we were taught ‘borrowing’, and being a moderately decent kid I always gave back what I borrowed.
I don't like the term 'carrying' because it refers to a superficial aspect of the method (that you carry the number from one place to another) rather than the essence of the operation.
When you add, 15+6, you add 5+6 to get 11, and then you regroup the 11 ones into 1 ten and 1 one.
When you subtract 21-6, you regroup the 2 tens into 1 ten and 10 ones. With the original 1 one, you now have 11 ones. Then you subtract the 6 from the 11 ones to get 5 as the last digit.
