From NAOJ and the National Museum of Nature and Science.
With fixed hours, an hour is the same length all year. With unequal hours, its length changes with the seasons. Today we use fixed hours, with 24 hours in a day.
Before mechanical clocks were developed, people divided the day into daytime and night, and split each one to set the time. Because the length of daytime changes with the seasons, the length of an hour changed with the seasons too.
In the Edo period, the time from ake-mutsu to kure-mutsu was divided into six to make one daytime koku, and the time from kure-mutsu to ake-mutsu was divided into six to make one night koku.
Names such as kokonotsu (nine) and yatsu (eight) were at first the number of drum beats that told people the time. Later they came to mean the times themselves.
Because “nine” or “six” alone was unclear, people added words such as hiru or ake, as in hiru-kokonotsu or ake-mutsu.
A clock measures time by using something that changes at a steady pace. Even so, clocks were invented that showed unequal hours on purpose, by changing their scales or their pace with the seasons or with day and night.
Tanaka Hisashige, an engineer active from the end of the Edo period to the early Meiji era, spent about a year making the Myriad Year Clock (mannen-dokei), finished in 1851. It is a large, spring-driven clock 57 cm tall, decorated with cloisonné, lacquer and mother-of-pearl.
Each side of its six-sided head has a dial: unequal hours with movable plates, the 24 solar terms, the days of the week and the striking of the hours, the ten stems and twelve branches, the old calendar date and the phases of the moon, and a Western clock face. On top, a model shows the rising and setting of the sun and moon.
The National Museum of Nature and Science says that Japan could quickly bring in Western science and technology in the Meiji era because of the foundation of science and technology built in the Edo period, and that Tanaka Hisashige was a bridge between the two.
The 24-hour day with fixed hours came in with the calendar reform of the Meiji era. It was announced on the 9th day of the 11th month of Meiji 5 (1872) and used from 1873.
There is no single right answer. Talking it over with someone at home is a good way to learn.