Here's how I would try to do it. In one hour, the hour hand will move from the 2 to the 3, and the minute hand will do a complete rotation from the 12 back to the 12. It should be obvious that the minute hand needs to at least get to the 8 (where it will be opposite the 2) and can not get to the 9 (opposite the 3).
To get to the 8 takes 40 minutes. 40 minutes is 2/3 of an hour, so the hour hand will be 2/3 of the way between 2 and 3.
Now think "every minute, the hour hand will move 1/60 of the way between 2 and 3, and the minute hand will move 1/5 of the way between 8 and 9".
See if you can continue.