It doesn't matter if the mini-wave is right-handed or left-handed. The dancers just hold hands and walk forward 1/4 of a circle around that spot -- exactly half as far as if they were going to do a Trade.
Usually, more than one pair of dancers will be doing a Hinge at the same time. If four dancers start in a wave, and each half of the wave does a Hinge, the result will be a box. Note that the two dancers in the center of the wave must first drop hands, before each half can turn.
If four dancers start in a box, the result will be a wave. The two dancers who come together in the middle must take hands to complete the wave.
Note that in every case, if dancers start facing head walls they will end facing side walls, and vice versa. Starting from parallel waves facing head walls, the result of everybody doing a Hinge is two new waves facing side walls.