The answer couldn’t be “on,” for in the sentence “Don’t miss this opportunity on traveling to Japan,” the preposition “on” indicates the location of something or a position in close proximity to something. A positional relationship isn’t the intended sense in that sentence, though; the correct sense is to indicate belonging or a possessive relationship between the noun “opportunity” and the phrase “traveling to Japan” as object of the preposition. That sense is correctly supplied by the preposition “of”: “Don’t miss this opportunity of traveling to Japan.”