In a 12-hour clock, the hour and minute hands align or overlap precisely 22 times in a 24-hour day. This includes 11 occurrences during the first 12 hours (from 12:00 AM to 11:59 AM) and 11 occurrences during the next 12 hours (from 12:00 PM to 11:59 PM).
During the first 12 hours, the minute hand and the hour hand overlap exactly at 12:00 AM (midnight) and then every hour after that (1:05 AM, 2:10 AM, 3:16 AM, and so on). The last overlap in the first 12 hours occurs at 11:54 AM.
Similarly, during the second 12 hours, the minute hand and the hour hand overlap again at 12:00 PM (noon) and then every hour after that (1:05 PM, 2:10 PM, 3:16 PM, and so on). The last overlap in the second 12 hours occurs at 11:54 PM.
It's important to note that this calculation assumes an idealized scenario with a clock that has perfectly synchronized hands and does not consider any seconds or fractions of a second.