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This old Buddhist phrase means, “When the sun rises it always shines first on the highest mountain,” or “When the sun appears, it first casts its light upon the highest mountain.”
This comes from the Avatamsaka Sutra and has been used as the name or portion of the name for temples in Japan and sites in China.
The Buddha's first round of teaching (Avatamsaka period) is likened to the time when the sun rises from the east horizon. When the sun first rises it illuminates the high mountains. In this analogy, the high mountains represent the great Bodhisattvas and/or those most ready to receive enlightenment and liberation.
This can be romanized from Japanese as “Nichi shutsu sen shō kō san,” “Nisshutsu saki teru takayama,” or “Hide temazu kōzan wo terasu yama.” The last one is probably the most common. Ask three Japanese people what they think the pronunciation is, and you will get three different opinions.