At what time between 2 and 3 o'clock will the hands of a clock be together?

At 2 o'clock, the hour hand is at 2 and the minute hand is at 12,  they are 10 min spaces apart.

To be together, the minute hand must gain 10 minutes over the hour hand.

Now, 55 minutes are gained by it in 60 min.

10 minutes will be gained in (60 x 10)/55 min. = 120/11 min.

The hands will coincide at 120/11 min. past 2.