If you back up the log only from 6 am to midnight, then the very first log backup at 6 am backs up all database activity that occurred 6 hours after the last log backup.
This is completely normal and probably has nothing to do with the fact that the database is backed up at 4 a.m.
Since you are on SQL2008, the warning in my other answer does not apply, and you should be good at working with log backups for 24 hours.
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