The question asks which of the given hills is located in the easternmost part of India. Let's analyze the options provided:

• Jaintia Hills: These hills are situated in the northeastern region of India, specifically in the state of Meghalaya. While they are located in the eastern part of the country, they are not the easternmost.
• Garo Hills: Like Jaintia Hills, Garo Hills are also located in Meghalaya. They too are in the northeastern region but are not the easternmost.
• Patkai Bum Hills: These hills are part of the Patkai mountain range and are situated along the northeastern margin of India covering parts of Arunachal Pradesh and touching Myanmar's border. They are indeed in the easternmost region among the options listed.
• Khasi Hills: Located in Meghalaya as well, Khasi Hills are part of the northeastern terrain but are not as far east as the Patkai Bum Hills.

Considering the location descriptions, the Patkai Bum Hills are the easternmost among the options provided. Therefore, the correct answer is:

Patkai Bum Hills