Apologies for not posting the answer last weekend, I was traveling.

This was perhaps too simple a puzzle, and that is why I did not get a response from anyone!

The correct answer is 22. An easy way to think about this is that from 1 to 2 pm (or am), the hands would overlap once, just after 1.05. Similarly between 2 and 3 pm, they will overlap once, again just after 2.10. This goes on..until between 10-11 pm. However, between 11 pm and 1 am, this happens only once, exactly at 12 am. Therefore in any 12 hour cycle, the clock hands overlap 11 times, hence in 24 hours, the clock hands overlap 22 times.

Hope you enjoyed the puzzle!