The four Farthings were four of the five (later six) divisions of the Shire. They were known simply as Northfarthing, Westfarthing, Southfarthing and Eastfarthing. The Westron word was Tharni, the Sindarin word (presumably) Canath.
Tolkien took the idea from the thridings in North Yorkshire, Northriding, Westriding and Eastriding. "Farthing" was used in Gloucestershire. Tolkien does not mention this in Nomenclature, but it is likely he knew of its existence as his wife Edith Bratt was born in Gloucestershire.