The question asks about a movement that emerged in 12th century Karnataka, led by Basavanna, and the name of his followers. To correctly answer this, let's explore some key historical facts:

1. Basavanna was a significant religious and social reformer in Karnataka during the 12th century.
2. He was a minister in the court of the Kalachuri ruler Bijjala I and is credited with founding the Lingayat sect, which aimed at promoting equality and social justice, opposing the rigid caste system by promoting the power of personal devotion to Lord Shiva.
3. The followers of Basavanna were known as Virashaivas or Lingayats. They rejected the traditional Brahmanical Hindu rituals and advocated for a direct relationship with God through the worship of Shiva in the form of a linga.
4. Basavanna and his followers emphasized social reforms, vegetarianism, and the abandonment of all forms of superstition.

Explanation of Options:

• Virashaivas: Correct option, as they were the followers of Basavanna.
• Pushtimargis: This sect was founded by Vallabhacharya in the late 15th century, focusing on the bhakti of Lord Krishna, not related to Basavanna.
• Avadhoots: This term generally refers to ascetic monks in Hinduism who transcend worldly attachments, widely seen in various traditions but not specifically linked to Basavanna.
• Nathpanthis: A Shaivist sub-sect associated with the Nath tradition and Gorakhnath, having a different spiritual lineage and therefore not connected to Basavanna's movement.

Therefore, the correct answer is: Virashaivas.