How can you subtract two integers without number lines or counters

For example:

12 - 10 = ?

Start with the numbers to the far right; take your 2 from the 12 draw a curving line from that 2 to the 0 in 10; ask what is 2 minus zero? 2!

Draw a curving arrow from the 1 in 12 to the 1 in 10. And ask, what is one minus one?

Zero.

Try that with other numbers