This is a heximal clock, optimized to make sense for a base-6 (heximal) number system.
In particular, the day is 100₆ (36⏨) hours, each hour is 100₆ (36⏨) minutes, and each minute is 100₆ (36⏨) seconds. This makes time math trivial; if a movie is 142₆ minutes long, it's 1₆ hour 42₆ minutes long (versus being 2hr 22min long in our current kinda-base-10-kinda-base-60 time system).
Each hex hour is 40 old-minutes long; each hex minute is about the same length as an old minute; each hex second is nearly two hex-seconds long. This means time periods are fairly similar; each unit should still be useful for the same sort of things that they're useful for today.
A notable change is the two hour hands. 36⏨ hours in one rotation is a big change from 12⏨, and knowing the exact hour is pretty important. To help this, the shortest hour hand points to the sixes digit of the hour, and the longer hour hand points to the ones digit of the hour; Because knowing the exact minute or second isn't nearly as important (and anyway, they've shrunk from 60⏨ to 36⏨ per rotation!), they both continue using a single hand each, like our existing clocks.
Paired with the heximal calendar, dates and times both become properly (heximal) metric, with successive units being a simple 1:100₆ ratio! See the blog post for more information and justification.