Final answer:
Buddhism had waves of contact with the West through different periods in history. These waves included contact during the Han times in China, through trade routes in Southeast Asia and the Silk Roads, and the sponsorship of Buddhism by King Ashoka and the Kushan Empire.
Step-by-step explanation:
Buddhism had several waves of contact with the West throughout history. The early stages of contact happened during the Han times in China, where Buddhism was initially mixed with Daoism. Missionary monks established communities in Loyang around AD 150, translating and teaching Buddhist texts. In Southeast Asia, Buddhism spread through trade routes and the arrival of Indian elites and literate Buddhists who became advisors to the region's powerful chiefs. Buddhism also spread through the Silk Roads between northern India and China, with Buddhist monks establishing monasteries in oases along the Taklamakan Desert. The spread of Buddhism continued to regions as far as the Kushan Empire in Central Asia, reaching China in the second century. Indian King Ashoka and the Kushan Empire also sponsored Buddhism, promulgating its faith and art. The influence of trade and Buddhism in East Asia was strengthened by the Tang dynasty and the expansion of trade routes.