The correct answer is C. Buddhist monasteries.
In the past, the education system of Ladakh was completely dependent on Buddhist monasteries. The monasteries were the only institutions that provided education in Ladakh. They taught the children the Buddhist scriptures, as well as other subjects such as mathematics, logic, and medicine. The monasteries also played an important role in the social and cultural life of Ladakh. They were centers of learning and scholarship, and they also provided social welfare services such as healthcare and education.
Ancient temples and schools run by the kings were not as important in the education system of Ladakh. The temples were mainly used for religious purposes, and the schools run by the kings were only available to a small number of children.
Therefore, the correct answer is C. Buddhist monasteries.