How many times from 4 pm to 10 pm, the hands of clock will be at right angle:

11

Two right angles are formed during each hourly period 4-5, 5-6, 6-7, 7-8, 8-9.

However, when the clock reaches 9pm, this coincides with the second 90° between the hours of 8-9. The clock has then to reach approximately 9.34pm for the only occasion when the hands will be at 90° in the hour 9-10.

So, 11 times from 4 pm to 10 pm, the hands of clock will be at right angle