The correct answer is option 3, Hazira.

Option 1, Jamshedpur is incorrect. Jamshedpur is a city in the state of Jharkhand, India, and is known for being the headquarters of Tata Steel. It is not the location of India`s first private sector Howitzer gun-making unit.

Option 2, Kolkata is incorrect. Kolkata is the capital city of the state of West Bengal, India. While Kolkata is known for its industrial and manufacturing sectors, it is not the location of India`s first private sector Howitzer gun-making unit.

Option 3, Hazira is correct. Hazira is a town located in the Surat district of the state of Gujarat, India. India`s first private sector Howitzer gun-making unit is located in Hazira. This facility is operated by Larsen & Toubro (L&T), a prominent Indian multinational conglomerate.

Option 4, Gwalior is incorrect. Gwalior is a city in the state of Madhya Pradesh, India. It is known for its historical and cultural significance, but it is not the location of India`s first private sector Howitzer gun-making unit.

Therefore, the correct answer is option 3, Hazira.