Making change

The question

Change from 10¢

How it works.

price:4¢

handed over:10¢

4¢+ 6¢→10¢

6¢

01
Two numbers matter and neither is a coin on the tray: the price, 4¢, and what was handed over, 10¢. Everything else is for afterwards.
02
Count UP from the price, not down from the payment. It is one hop here: 4¢ to 10¢. Done as a take-away this is where the borrowing goes wrong; counting up there is nothing to borrow.
03
That one hop IS the change: 6¢. Now find coins that make that amount.