As mentioned in the initial description, this clock uses epicyclic gearing to provide the 60:1 and 12:1 reduction ratios between seconds and minutes and between minutes and hours. This is described in my DIY Skeleton Epicyclic Clock with 3D Printed Gears but I shall repeat it here.
The principle involved is that when a pinion is moved round two spur gears with just one tooth difference and one gear is fixed the moving gear rotates by one tooth for each revolution of the axis of the pinion. So if the fixed gear has 59 teeth and the moving gear 60 teeth the gear ratio between the rotation of the pinion axle and the moving gear is 60:1. This is the ratio required for seconds to minutes in a clock.
When the gears are different by two teeth the moving gear turns by two teeth for each revolution of the pinion axle thus if the gears have 22 and 24 teeth the gear ratio becomes 24:2 = 12:1. This is the minutes to hours ratio. However, it works out better to have more teeth and a lower modulus to make the motion smoother for 3D printed gears. Using 44 and 48 teeth gives a gear ratio of 48:4 = 12:1.