Final answer:
The correct answer is option a) Protectorate.
Step-by-step explanation:
A protectorate is a colony administered by local rulers with guidance and assistance from European advisors. In this system, the local rulers remain in nominal control while receiving protection from a foreign power. In exchange for this protection, the foreign power often receives exclusive trading rights or other benefits. This was a common form of administration during the era of European colonial expansion.
Comparatively, in the case of imperialism, a country extends its power and influence through diplomacy or military force, often leading to direct rule or annexation of territories. Annexation involves incorporating a territory into another state, and direct rule is when the governing authority oversees the colony without intermediaries or local governance structures.