Answer:
The two territories of the Ottoman Empire that became British territories because of League of Nations mandates were Palestine and Mesopotamia (present-day Iraq).
The League of Nations, which was established after World War I, was responsible for assigning mandates to various colonial powers to administer former territories of the defeated Ottoman Empire. The League of Nations mandate for Palestine was granted to the British in 1922, and the mandate for Mesopotamia was granted to the British in 1920.
Under these mandates, the British were responsible for administering the territories and promoting their development, with the eventual goal of preparing them for self-rule. However, the mandates were controversial and faced resistance from local populations, particularly in Palestine, where tensions between Jewish and Arab communities complicated British efforts to govern the territory.