The question tests knowledge about the location of certain famous monasteries in India.

Dhankar Monastery and Tabo Monastery both are correctly matched with Himachal Pradesh as these are located in this state. Rumtek Monastery is also rightly matched with the state of Sikkim; it is one of the largest and most significant monasteries in Sikkim.

The 4th option is incorrect. The Kye Monastery, also known as Ki, Kye or Kee, is wrongly matched with Arunachal Pradesh. In fact, the Kye Monastery is located in Himachal Pradesh, not in Arunachal Pradesh. It is a Tibetan Buddhist monastery located in the Spiti Valley of Himachal Pradesh.

So, the mismatch in the pair in option 4 makes it the correct answer to the question, "Which pair is not correctly matched?" as asked in the question.