The pilgrimage to the holy Amarnath cave takes place during the Hindu month of:

Kartik
Shravan
Chaitra
Magh

The correct answer is: b) Shravan.

The Amarnath Yatra is a Hindu pilgrimage to the Amarnath cave shrine in the Indian state of Jammu and Kashmir. The cave is situated in a Himalayan cave at an altitude of 3,880 metres (12,730 ft) and is revered by Hindus as the abode of Shiva. The pilgrimage is undertaken during the Hindu month of Shravan (July–August), when a natural ice stalagmite is believed to form a lingam, a representation of Shiva.

The pilgrimage is a challenging one, as it involves trekking through a high-altitude mountain pass. The route is also prone to landslides and avalanches. However, the pilgrimage is considered to be a very auspicious one, and thousands of pilgrims undertake it every year.

The other options are:

a) Kartik: The Hindu month of Kartik is the month of Diwali, the festival of lights. It is a time for family and friends to come together and celebrate the victory of good over evil.

c) Chaitra: The Hindu month of Chaitra is the first month of the Hindu calendar. It is a time for new beginnings and fresh starts.

d) Magh: The Hindu month of Magh is the third month of the Hindu calendar. It is a time for bathing in holy rivers and fasting.