Final answer:
The provincial or royal colony was the most tightly controlled by the British crown with a Crown-appointed governor and veto power over the legislature's decisions. Therefore, the correct option is d. provincial colony.
Step-by-step explanation:
The type of colony that was the most tightly controlled by the British crown was the provincial colony, essentially another term for a royal colony. In a royal colony, the Crown appointed the governor and could veto any decisions made by the colonial legislature.
This system allowed the British to maintain significant oversight and control over colonial governance, compared to proprietor or corporate colonies where the governor was selected by proprietors with Crown's approval or by the voters, respectively.