The hands of a clock coincide when they are at the same position on the clock face. To determine how many times the hands of a clock coincide in a day, we need to consider the movement of the hour hand and the minute hand throughout the day.

1. Hour Hand Movement:
- The hour hand completes one full revolution in 12 hours.
- So, it moves 360 degrees in 12 hours.
- Therefore, the hourly movement of the hour hand is 360/12 = 30 degrees.

2. Minute Hand Movement:
- The minute hand completes one full revolution in 60 minutes.
- So, it moves 360 degrees in 60 minutes.
- Therefore, the hourly movement of the minute hand is 360/60 = 6 degrees.

Now, let's analyze the coinciding positions of the hour and minute hands.

- The hands of a clock coincide at exactly 12 o'clock.
- After 1 hour, the minute hand moves 6 degrees, while the hour hand moves 30 degrees.
- The difference in their positions is 30 - 6 = 24 degrees.
- The hands will coincide again when the minute hand catches up to the hour hand by this difference of 24 degrees.
- The minute hand takes 60 minutes to cover this difference of 24 degrees.
- Therefore, the hands of the clock coincide after every 60 minutes.

To find the total number of times the hands of a clock coincide in a day, we need to determine how many sets of 60 minutes are there in a day.

- In 24 hours, there are 24 sets of 60 minutes.
- Therefore, the hands of the clock coincide 24 times in a day.

So, the correct answer is option D) 22.