The correct answer is option 3: Meghalaya.

To understand why this option is correct, we need to examine the geography of Myanmar and the surrounding Indian states. Myanmar shares borders with several Indian states, including Arunachal Pradesh, Nagaland, and Mizoram. However, Meghalaya does not share a direct border with Myanmar. Instead, Meghalaya is located to the south of Assam, which does have a border with Myanmar.

It is important to note that the other options, Arunachal Pradesh, Nagaland, and Mizoram, do share a border with Myanmar. Therefore, in this context, Meghalaya is the state that does not border on Myanmar.

Alert - correct answer should be option 2: Nagaland. Since Nagaland is the only state that does not share a border with Myanmar.