There are 9 hours between 9pm and 6am.
Solution:
Since the times cross from pm to am, use midnight (12:00am) to help us count the time.
9:00 am is 3 hours before midnight.
6:00 pm is 6 hours after midnight.
Time difference = Time from 9:00pm to midnight + Time from midnight to 6:00 pm
Time difference = 3 hours + 6 hours
Time difference = 9 hours
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