The hour, minute, and second hands of a clock with continuous sweeping can never be spaced at exactly 120° intervals. This was shown in

Part 1
Find the exact time when these angles are as close as possible and the order of the hands are hour, minute, second in a clockwise fashion.

['As close as possible' means the sum of the individual deviations from 120° is minimized.]

I have not followed Charlie's derivation in detail, but he seems to propose 02:54:34 and 09:05:25 as approximate solutions. As I read the specs, the solution must satisfy the condition not only of approx equal angles but also "and the order of the hands are hour, minute, second in a clockwise fashion." I assume "clockwise fashion" means that the clock runs to the right hand (not "backwards"), and visually starting at 00:00:00 the hour hand comes first, then 120 degrees later the minute hand, and then a further 120 degrees later the second hand. In Charlie's main solution the minute hand is after the second hand; and in the reflection (?) solution, the hour hand is after both the minute and second hands.

How is the "order of the hands" constraint being interpreted?