Step 1: Identifying the marked region.
The map in the question marks Awadh (Oudh) in northern India. Awadh was an important princely state during the British colonial period and had close political relations with the East India Company.
Step 2: British expansion policies.
The British used several policies to expand their control in India, such as the Doctrine of Lapse, Subsidiary Alliance, annexation through wars, and annexation on the pretext of misgovernance. These policies allowed the British to gradually take control of many Indian states.
Step 3: Annexation of Awadh.
Awadh was annexed by the British in 1856 by Governor-General Lord Dalhousie. The British claimed that the administration of Awadh was inefficient and corrupt, and they used the pretext of misgovernance to justify its annexation.
Step 4: Conclusion.
Since Awadh was annexed by the British citing poor governance as the reason, the correct policy of expansion used in this case was the pretext of misgovernance.
Final Answer: Pretext of misgovernance.