There's no single answer to "How many days is June 15?" It depends on what you're asking:
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Days remaining in June: If you're asking how many days are left in June after June 15th, there are 15 days remaining (30 total days in June - 15 days already passed = 15 days left).
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Days since the start of June: If you mean how many days have passed in June up to and including June 15th, then the answer is 15 days.
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Days in a specific year: The number of days in June is always 30. June 15th is always the 15th day of June, regardless of the year.
To clarify your question, please specify what you want to know: the number of days remaining in June after June 15th, the number of days that have passed in June up to and including June 15th, or something else.