How many times do the digits of a digital clock add up to 6 in a 12 hour period?

The short answer is "27" and we have to make a number of assumptions because the question as described enough is vague.

So let us assume:
- we are only considering a clock displaying HH:MM where HH is hours and MM is minutes.
- we start the 12 hour period at 00:00 (midnight).
- we must add all 4 digits individually.  So 11:11 is 1+1+1+1 not 11+11
- The sum of all 4 digits must equal 6

01:05
01:14
01:23
01:32
01:41
01:50
02:04
02:13
02:22
02:31
02:40
03:03
03:12
03:21
03:30
04:02
04:11
04:20
05:01
05:10
06:00
11:04
11:13
11:22
11:31
11:40

If you start the clock at midday then the options are:
12:03
12:12
12:21
12:30
13:02
13:11
13:20
14:01
14:10
15:00
20:04
20:13
20:22
20:31
20:40
21:03
21:12
21:21
21:30
22:02
22:11
22:20
23:01
23:10

step-by-step explanation:

yes it is1. move over 2 points on the x-axis2. move over 2 points on the y-axis