I'm now not sure if the hinge relates to the hands or shoulders or both. Until I get some time to practise it, then the penny might drop ?
TGM uses the door hinge analogy as a way to describe the movement of the club face, thru impact. The Horizontal hinge is demonstrated by a door, which hinges in the horizontal plane. A Vertical hinge can be described by a dog door, which hinges in the vertical plane.
The hinges can be replicated by the shoulders, arms and wrist.
A Horizontal hinge is replicated by turning shoulders, while standing upright and with the arms extended outward in a horizontal position. The arms can also replicate this hinge, without turning the shoulders. While keeping the arms in the extended horizontal position, a Vertical hinge can be replicated by rotating the forearms.
If the arms are held downward, as near to parallel to the legs, a Vertical hinge can be achieved with the wrists. However this action will compromise the Flat Left Wrist and not terribly useful accept for creative shots, like those used around the green.
Because the golf swing happens on an inclined plane, the golfer has to combine those two actions, to achieve the desired hinge angle. The best way to understand how the mechanics work is to go out and practice some pitching and chipping, while monitoring what is happening with the shoulders, arms and forearms.