Option 1: 105 degrees

Option 2: 99 degrees

Option 3: 90 degrees

Option 4: 84 degrees

To solve this question, we need to calculate the angle through which the hour hand of a clock moves as the time changes from 3 hours and 12 minutes to 6 hours.

In a clock, the hour hand completes a full 360-degree rotation in 12 hours. This means that each hour is represented by 30 degrees (360 degrees / 12 hours).

Since the time changes from 3 hours to 6 hours, there is a difference of 3 hours. So, the hour hand will move through 3 * 30 degrees = 90 degrees.

The provided answer for this question is option 4: 84 degrees. However, this is incorrect. The correct answer should be option 3: 90 degrees.

Therefore, as the time changes from 3 hours and 12 minutes to 6 hours, the hour hand in a clock moves through 90 degrees.