Which type of fastener uses a penny system to indicate its size?

The correct answer is finishing nail, as this type of fastener utilizes the penny system to denote its size. The penny system, often represented by the abbreviation "d" (for "penny"), was a historical reference to the price for which a certain quantity of nails would sell. Hence, a 1d finishing nail is smaller than a 16d nail. The measurement in the penny system is based on the length of the nail in inches, where traditionally, the larger the number, the longer the nail.

The other options do not adhere to the penny system. A carriage bolt is sized by its diameter and length but does not use this historical pricing reference for its size. A lock washer and a drill bit also have their own sizing systems related to their specific functions and uses, but they do not correspond to the penny system like finishing nails do.