Under which dynasty did china control territories that are not part of modern china?

It happened during Han dynasty. The emperors of the Han Dynasty (207 BC-AD 220) imposed Confucianism and created a network of high-trust officials called "mandarins". They maintained the administrative structure of the Chin, but they suppressed its authoritarian character.

Han China expanded its borders by incorporating what is now Tibet, North Korea and part of Vietnam. An active trade was developed with the northern neighbors, as well as with Europe, through the "Silk Road". In education and science there was a time of blossoming. In addition, from India was introduced Buddhism (philosophical and religious system based on the teachings of the Buddha).

d is definitely the answer