The correct answer is option 3: 24 minutes past 2.

To understand why this is the correct answer, let`s analyze the problem. The question asks for the time when the hour and minute hands of a clock will be 12 minute divisions apart between the hours of 2 and 3.

In one hour, the minute hand travels 360 degrees, while the hour hand travels 30 degrees. This means that for every minute that passes, the minute hand moves 6 degrees and the hour hand moves 0.5 degrees.

To find the time when the hands are 12 minute divisions apart, we need to calculate the angle between the hands. The angle can be found using the formula: angle = (11/2) * (hour - minute), where the hour is represented in hours and the minute is represented in minutes.

Setting the angle equal to 12 and solving for hour, we get:

12 = (11/2) * (hour - minute)

Now, let`s plug in the values for hour and minute between 2 and 3:

When hour = 3 and minute = 24, the equation becomes:

12 = (11/2) * (3 - 24)

12 = (11/2) * (-