The script of ancient India that was written from right to left is Kharoshti. This script was primarily used in the northwestern regions of India from the 3rd century BCE to the 3rd century CE.

Option 1, Brahmi, was incorrect as it was written from left to right. It is one of the oldest writing systems used in the Indian Subcontinent.

Option 2, Nandnagari, was also written from left to right. It is a later variant of the Brahmi script and was not as broadly used as the other options listed.

Option 3, Sharada, was likewise written from left to right. It was used in Kashmir and neighboring regions during the 8th to 12th centuries.

Therefore, option 4, Kharoshti, is the correct answer as it is the only script listed that was written from right to left.