$\textbf{Answer}$

$22$

$\textbf{Analysis}$

Starting from $12:00$ (when the two hands overlap the first time), the minute hand always moves faster than the hour hand does. Therefore, there will be no overlap till $1:00$. Then, sometime between $1:00$ and $2:00$, the minute hand will catch up the hour hand when these two overlap. Similarly, they will overlap again at $2:xx$, $3:xx$, $\cdots$, $10:xx$ where $xx$ indicates some minutes. Please note that there are no such moment as $11:xx$ when the two hands overlap. This is because after $11:00$, the next time they meet will be $12:00$ exactly. Therefore, the two hands will meet $11$ times starting from $12:00$ till, but excluding, the next $12:00$. It follows that the final answer is $22$ times.

$\textbf{Note}$

Always be careful about the boundary conditions. In this case, the most common incorrect answer is $24$.