Step 1: Place Nirukta in the Vedangas.
The six Vedangas are shiksha, kalpa, vyakarana, nirukta, chhanda and jyotisha. Nirukta is the one that deals with word origin and meaning.
Step 2: Match each name with a work.
Panini goes with the Ashtadhyayi and Bhartrihari with the Vakyapadiya. Kautsa is a critic who is named inside the Nirukta, not its author.
Step 3: Recall the author.
Yaska wrote the commentary on the Nighantu, and this work is called the Nirukta.
Step 4: Choose.
The author Yaska is option 2.
Step 5: Second check.
Remember the pair Yaska and Nirukta, just like Panini and Ashtadhyayi. Yaska is also known for naming four classes of words: noun, verb, preposition and particle. Keeping this pairing in mind makes the question easy. The other names in the options are linked with other works, so option 2 stays correct after a second check.
Final Answer:
Yaska composed Nirukta, option 2.
\[\boxed{\text{Option 2}}\]