"India Conquered and dominated China culturally for 20 centuries without ever having to send a single soldier across her border"

Hu Shih is suggesting that India's cultural influence on China was so strong that it achieved domination and control over the Chinese people without any military intervention. This means that India's civilization, faith, art, literature, viewpoint, education, and customs had such an influence on China that it formed its way of living, beliefs and values for two centuries. India's soft power was so reliable that it did not require to dominate China by force or violence, but rather by the power of concepts and culture.