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

Answer: 12:11pm.

Since the watch is losing 6 minutes every hour, for every real hour that has passed, the watch will only show 54 minutes (i.e. for every 54 clock minutes, 60 real minutes have passed)

Since the watch shows 10:39am we know:

10:39am = (10 x 60) + 39 = 639 watch minutes

for every 54 watch minutes, 60 real minutes have passed:

(639 ÷ 54) x 60 = 710 real minutes

and converting this to hours:

710 minutes = 11 hours 50 minutes

the watch stopped 21 minutes ago, so the current time is:

12.11pm. QED.

Puzzle 999

Gib is to llams as nepo is to desolc as pu is to ==?==