The correct answer is (a) Amravati.
The Satavahanas were an Indian dynasty that ruled over a large part of the Indian subcontinent from the 2nd century BCE to the 3rd century CE. Their capital was located at Amravati, which is now a city in the Indian state of Maharashtra.
Amravati was an important center of trade and culture during the Satavahana period. It was also a major Buddhist center, and many Buddhist stupas and monasteries were built there.
The Satavahanas were a powerful dynasty that played an important role in the history of India. They were patrons of art and literature, and their rule saw a flowering of Indian culture.
The other options are incorrect.
(b) Nanded is a city in the Indian state of Maharashtra. It was not the capital of the Satavahanas.
(c) Naldurg is a town in the Indian state of Maharashtra. It was not the capital of the Satavahanas.
(d) Durg is a city in the Indian state of Chhattisgarh. It was not the capital of the Satavahanas.