The correct answer is option 2, Bakhtiyar Khilji. Bakhtiyar Khilji was the first Muslim military commander who annexed Bihar and Bengal by overthrowing the Sena dynasty.

Option 1, Mahmud Gawan, is incorrect. Mahmud Gawan was a prominent Bahmani statesman and scholar who served as the prime minister in the Bahmani Sultanate.

Option 3, Adil Shahis, is incorrect. Adil Shahis were a dynasty that ruled the Bijapur Sultanate in present-day Karnataka, and they were not involved in the annexation of Bihar and Bengal.

Option 4, Shams-ud-Din, is incorrect. There is no historical figure by the name Shams-ud-Din who is associated with the annexation of Bihar and Bengal.

It is important to note that while Bakhtiyar Khilji is generally attributed as the commander who annexed Bihar and Bengal, there is some historical debate and controversy surrounding the exact details of this conquest. However, Bakhtiyar Khilji is commonly recognized as the first Muslim military commander to overthrow the Sena dynasty in that region.