Panini, the first Grammarian of Sanskrit language, lived during the 6th-5th Century B.C. This period is also known as the Vedic period, which was characterized by the flourishing of ancient Indian culture and the development of the Sanskrit language. Panini`s work, known as the Ashtadhyayi, is considered one of the most important and comprehensive treatises on Sanskrit grammar.

Option 1, 2nd Century B.C, is not the correct answer. Panini lived much earlier than the 2nd Century B.C.

Option 3, 2nd Century A.D, is also not the correct answer. Panini lived much earlier than the 2nd Century A.D.

Option 4, 5th-6th Century A.D, is not the correct answer either. Panini lived much earlier than the 5th-6th Century A.D.

Therefore, the correct option is 2, 6th-5th Century B.C, as it accurately represents the time period in which Panini lived and contributed to the development of Sanskrit grammar.