How many times do the hands of a clock coincide in a day?

The hands of a clock (the hour hand and the minute hand) coincide exactly once every $\frac{12}{11}\text{ hours}$ (approximately every $65\text{ minutes and }27.3\text{ seconds}$).
* In a $12\text{-hour}$ period, they coincide $11$ times (since the overlap between $11$ and $1$ occurs exactly at $12$ o'clock).
* In a full day ($24\text{ hours}$), they coincide $11\times 2=22$ times.