The hands of a clock form a 60 degree angle which two different times could it be?
The hands of a clock form a 60 degree angle twice every hour, once when the minute hand is 1/3 of the way between two numbers on the clock face and once when it is 1/3 of the way past the same two numbers.
For example, if it is 4:00, the minute hand will be at the 12 and the hour hand will be at the 4, forming a 60 degree angle. The same angle will be formed at around 20 minutes past the hour.
So, two different times when the hands of the clock form a 60 degree angle are:
1) At exactly 4:00
2) At around 4:20