Understanding the Question: The question asks for the specific suffix (Pratyaya) used to turn a verb into a form expressing obligation, necessity, or possibility (the gerundive).
Key Concepts and Approach: Suffixes added to verbal roots are called Kṛt Pratyayas. Some are used for past tense, some for infinitives, and others for the "potential" mood.
Detailed Solution:
Step 1: Analyzing Tavya. The Tavya (or Tavyat) suffix is part of the Kṛtya group. It is used to indicate that an action "ought" to be done. For example, Kṛ (to do) + Tavya = Kartavya (that which should be done).
Step 2: Comparing other suffixes.
Ktvā: used for "having done" (e.g., Kṛtvā).
Tumun: used for "to do/for doing" (e.g., Kartum).
Lyap: used for "having done" when there is a prefix (e.g., Saṃbhūya).
Step 3: Semantic identification. Only Tavya carries the "should" or "potential" sense required by the question.
Conclusion: The suffix is Tavya.