How did the Inca collect taxes in labour instead of money, and how did the Spanish twist it?

The Inca collected taxes in labour because their state ran on work, not on markets: commercial exchange between producers and buyers was not practised, and goods were managed by the central authority. The system was called the mit'a, a word that basically means a regular 'turn' or 'season'. All citizens who could work were required to do so for a set number of days a year. Tax labour accounted for much of the Inca state's revenue, and it built and kept up the road network, bridges, farming terraces and fortifications.

It had rules that made it bearable. All males from age fifteen to fifty took part, and overseers were responsible for making sure a man still had time to care for his own land and family. The state's storehouses supplied mit'a workers on big projects such as roads. Most people did their turn in or near home, often in farming, and mine service was extremely rare.

Then the Spanish arrived and kept the name. In 1573 the Spanish Crown repurposed the mit'a, drafting one-seventh of the adult male population to work in mines. Under viceroy Francisco de Toledo it expanded to feed the great silver mine of Potosí.

The two systems served different purposes. The Inca mit'a provided public goods, such as roads and irrigation. The Spanish mit'a subsidised private mining interests and a state that used the silver largely to finance European wars. It became an intolerable burden, with abuses, complaints and revolts. A form of mit'a is still alive: in small Quechua communities it survives as faena.