When did Shinto merge with Buddhism in Japan?

a date would be nice

Probably close to 2000 years ago.

It didn't. There is no exclusivity in eastern religion (unlike Christianity, Islam, etc.). One can be a Buddhist and a Shinto at the same time.

During the rule of Prince Shotoku (7Th century AD). He was a great admirer of China and Buddhism flourished in his court. Although both Shinto and Buddhism maintained their separate ideas, Buddhism adapted well because it appealed to the Japanese spiritual mindset.

No specific date can be given, but Shinto began incorporating Busddhism as soon as Buddhism arrives int he 6Th Century, AD.

Prince Shotoku (574-622) is the fonder of Buddhism in Japan, and was largely responsible.