1. Kashmir Himalayas
2. Himachal Himalayas
3. Darjeeling Himalayas
4. Arunachal Himalayas

The correct answer is option 'A', which means that the correct arrangement of the Himalayan sub-divisions from west to east is 1, 2, 3, 4. Let's understand why this is the correct answer.

1. Kashmir Himalayas:
- Located in the westernmost part of the Himalayan range, it extends from the Indus River in the west to the Kali River in the east.
- Major states and regions covered include Jammu and Kashmir and some parts of Himachal Pradesh and Uttarakhand.
- Prominent peaks in this region include Nanga Parbat, Haramukh, and Trisul.

2. Himachal Himalayas:
- Located to the east of the Kashmir Himalayas, it covers the entire state of Himachal Pradesh.
- The region is known for its beautiful valleys, high mountain passes, and trekking routes.
- Some of the famous peaks in this region include Kinner Kailash, Deo Tibba, and Hanuman Tibba.

3. Darjeeling Himalayas:
- Located further east, this sub-division is known for its picturesque hill stations and tea gardens.
- It covers the Darjeeling district of West Bengal and extends into parts of Sikkim and Nepal.
- The region is famous for its panoramic views of Mount Kanchenjunga, the third-highest peak in the world.

4. Arunachal Himalayas:
- Located in the easternmost part of the Himalayan range, it covers the state of Arunachal Pradesh.
- This region is characterized by its rugged terrain, deep valleys, and dense forests.
- It is home to several peaks, including Kangto, Nyegi Kangsang, and Gorichen.

Therefore, the correct arrangement of the Himalayan sub-divisions from west to east is 1. Kashmir Himalayas, 2. Himachal Himalayas, 3. Darjeeling Himalayas, and 4. Arunachal Himalayas.