Note: its a standard 12 division clock as below. Example:

11
22
23
24
12

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Observation:

In every hour 90 degree is formed twice except for between 2 to 3 o'clock and 8 to 9 o'clock where it is formed only once. So the answer is 12 * 2 - 2 = 22.

Mathematical approach:

At 3:00 we see a 90 degree. Lets assume after x minutes we will see another 90 degree with same orientation (from the same side). In 1 minute the minute hand moves x * 360/60 = 6x degree. In 1 minute the hour hand moves x * 360/(12*60) = x/2 degree. The minute hand will rotate 360 degree more than the hour hand. So we get,

6x = x/2 + 360

=> x = 2 * 360/11

so in 12 hours, we see it [12 * 60 / (2 * 360/11)] times = 11 times.

Similarly, at 9:00 we see a 90 degree but in different orientation. Doing the same calculation, we get another 11.

So total number of times 90 degree is formed is 11 + 11 = 22 times.