Hint: For every real hour, how many watch minutes pass?

Answer: 10.00am.

Since the watch is losing 20 minutes every hour, for every real hour that has passed, the watch will only show 40 minutes. Since the watch shows 4.00am, we know that 240 watch minutes have passed. This therefore equals 360 real minutes and hence 6 hours. The watch stopped 240 minutes ago, therefore the time must now be 10.00am. QED.