The correct answer is option 4, the Rastrakutas. The Empire of Chalukyas of Badami was located in present-day Karnataka, India, and existed from the 6th to the 8th century CE. The Chalukyas were a powerful dynasty and had extensive control over the Deccan region. However, their downfall came with the rise of the Rastrakutas. The Rastrakutas were a dynasty that originated in present-day Maharashtra, India, and they gradually expanded their territory through strong military campaigns. In the 8th century, under the leadership of their ruler Dantidurga, the Rastrakutas launched a series of attacks on the Chalukyas and managed to conquer and destroy their empire. The Rastrakutas went on to establish their own prominent empire, ruling over large parts of southern and central India for several centuries. It is important to note that while the Cholas, Pallavas, and Pandyas were contemporaries of the Chalukyas and significant dynasties in South India, they were not directly responsible for the destruction of the Chalukya empire.