The duchy that sheltered Edward IV after Warwick forced him into exile in 1470 was Burgundy.
Warwick, the Earl of Warwick and later-famous “Kingmaker,” had turned against Edward and helped restore Henry VI. Edward fled England in October 1470 with his youngest brother, Richard, Duke of Gloucester, and a small group of supporters. They crossed to the Low Countries, where Edward sought help from Charles the Bold, Duke of Burgundy.
Burgundy was not simply a passive refuge. Charles provided Edward with ships, money, weapons and troops, partly because Lancastrian control of England threatened Burgundian trade and political interests. Edward returned to England in March 1471, regained the throne after victories at Barnet and Tewkesbury, and Warwick was killed at Barnet.
A common mix-up is to answer “Flanders” or “the Netherlands.” Edward stayed in Burgundian territories, including the coastal town of Flushing, but Burgundy is the duchy named in the question and the canonical quiz answer.