The very first answer, above, by AD is correct. It's 44. The explanation given might be a bit complicated, so if you don't understand why it's 44 and not 48, just doing the following exercise will clear it up. Simply take an analog clock (or watch) and count the number of times the hands form a right angle as you turn them manually. The 90° angles occur 22 times in a 12-hour period, so you don't have to keep counting. Just multiply by 2 to get 44.

It's easy to believe that the right angles occur twice every hour, but not so. They appear twice every 65.44 minutes, so at the end of the 24-hour period, the 90° angles have only had enough time to occur 44 times. For visual evidence, the secret lies between 2 and 3 o'clock, and between 8 and 9 o'clock.

Source(s):
I figured it out mathematically, and tested it manually.