Final answer:
The country that revolted against Spanish rule under King Philip II in the late 16th century, leading to a major challenge for the king, was the Netherlands, specifically the northern provinces that later formed the Dutch Republic.
Step-by-step explanation:
A major challenge faced by King Philip II in the late 16th century was a revolt against Spanish rule by the country known today as the Netherlands. The provinces in the northern part of the Spanish Netherlands, which later became known as the Dutch Republic or Holland, initiated a rebellion. These provinces declared their independence from Spain in 1581 and fought a war against Spanish rule that continued until a truce in 1609. The conflict is notably marked by the failed Spanish Armada of 1588, which was assembled by King Philip II with the intention of ending Protestantism in the rebellious provinces, as well as England, which supported them.