Which of the following uses a penny system to specify its size?

The finishing nail is the correct answer because it is measured using a penny system, typically denoted by the term "d" where the size is indicated in terms of the number of pennies. For example, a 4d finishing nail is one that is 1.5 inches long, while a 6d finishing nail is 2 inches long. This penny sizing system is particularly common in the context of nails and is used to convey the length and sometimes the diameter of the nail in a simple shorthand.

Other types of screws listed, such as wood screws, sheet metal screws, and lag screws, do not utilize the penny system for size designation. Instead, they are typically measured by their gauge and length, which does not follow the same penny measurement metric as finishing nails.