Final answer:
The Mughal emperor recognized the right of the British East India Company to collect taxes in northeastern India primarily for military support and protection as the Mughal Empire was weakening, as exemplified by the British victory at the Battle of Buxar in 1764.
Step-by-step explanation:
The recognition by the Mughal emperor of the right of the British East India Company to collect taxes in northeastern India was largely due to military support and protection that the Company could provide to the weakening Mughal Empire. In 1764, British and Indian forces under the command of the British East India Company defeated a much larger army led by the Mughal emperor Shah Alam II at Buxar.
After this victory, the Mughals, while retaining control of northern and western India, effectively surrendered governance of much of southern and eastern India to the British East India Company. This included awarding the British East India Company the right to collect taxes in Bengal in 1765. The financial benefits from tax collection enabled the Company to further dominate India.
Moreover, the Company's policy of indirect rule and cooperation with Indian elites ensured a steady flow of taxes and military support with Indian soldiers known as sepoys, who were often led by British officers. This arrangement contributed significantly to the Mughals' decision to grant the British East India Company these crucial rights, which further solidified British presence and power in India.