Explanation:

Alright, let’s break this down:

- Option 1: Preaching in the common language of the people

Both Buddhism and Jainism spread their teachings using local languages (Pali for Buddhists, Prakrit for Jains), making them accessible. This was a deliberate move away from Sanskrit.

- Option 2: Drawing inspiration from the teachings of the Upanishads

Here’s where they split. While both existed in the same philosophical landscape, the Buddha and Mahavira weren’t directly inspired by the Upanishads. Buddhism even rejected many Upanishadic concepts like the atman (soul). Inspiration wasn’t a shared base.

- Option 3: Denouncing the caste system and advocating equality of men and women

Both criticized the rigid social order, and Buddhism particularly welcomed anyone regardless of caste or gender. Jainism also allowed for participation, though with some restrictions, but both challenged strict caste hierarchy.

- Option 4: Avoidance of extremities of penance and enjoyment

This is what really sets them apart. Buddhism talks about the “Middle Path” as a core principle—staying away from extreme self-indulgence and extreme self-mortification. Jainism, on the other hand, is famous for its intense asceticism and severe penances.

So, the correct answer is:

Option 4 is NOT common to both. Only Buddhism consistently avoids extremities; Jainism embraces them.