Which belife system spread first from india to china and then to korea, and japan, to create cultural unity in the region

Buddhism is the correct answer.

Developed from the teachings of Buddha, Buddhism is a religion and philosophy that started in India and spread to China, Korea, Japan, Central and Southeast Asia. The word Buddhism comes from 'buddhi' which means 'to awaken' and refers to the moment Buddha was awakened (or enlightened) when he was 35 years of age. It has played an important role in Asian cultures and spirituality around the world and unified different cultures. Buddhism is about explaining the purpose to life. It also explains injustice and inequality worldwide and provides a 'code of practice' that leads their followers to true happiness.  

it was on the rise and doing very well and would continue to do well until the great depression from 1929-1939