The hands of a clock coincide when they overlap or are in the same position. To determine how many times this happens in a day, we need to understand the movements of the hour and minute hands.

1. The minute hand:
- The minute hand completes a full revolution every 60 minutes.
- Therefore, it covers 360 degrees in 60 minutes or 6 degrees per minute.
- In one hour (60 minutes), the minute hand moves 360 degrees.

2. The hour hand:
- The hour hand completes a full revolution every 12 hours.
- Therefore, it covers 360 degrees in 12 hours or 30 degrees per hour.
- In one hour, the hour hand moves 30 degrees.
- In one minute, the hour hand moves 0.5 degrees (30 degrees divided by 60 minutes).

Now, let's consider the relative movements of the hour and minute hands.

3. Relative movements:
- The minute hand moves continuously, while the hour hand moves incrementally.
- The minute hand moves 6 degrees per minute, while the hour hand moves 0.5 degrees per minute.
- The relative speed of the hands is 6 - 0.5 = 5.5 degrees per minute.

To determine how many times the hands coincide, we need to find the number of times the minute hand gains a full lap on the hour hand.

4. Calculation:
- The minute hand gains a full lap (360 degrees) on the hour hand every 360 / 5.5 = 65.45 minutes.
- Since there are 60 minutes in an hour, the minute hand gains a full lap on the hour hand approximately every 65 minutes.
- This means that the hands coincide approximately 22 times in a 24-hour day (24 * 60 minutes divided by 65 minutes).

Therefore, the correct answer is option C) 22. The hands of a clock coincide approximately 22 times in a day.