The number of times in a day the Hour hand and the Minute hand of a clock at right angles is

In every 12 hour period, the minute hand and hour hand form a 90 degree angle twice every hour. However, there is a catch. Between 2 and 4 o clock, and between 8 and 10 o clock, the hands are at right angles only 3 times instead of 4. This is because the right angle exactly at 3 o clock and 9 o clock is shared between the two hours.

Therefore, in a 12 hour cycle, the hands are at right angles 22 times. Since a full day has 24 hours, you multiply 22 by 2, which equals 44.