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When the dancers are in a mini-wave, the action of Cast Off 3/4 is an Arm Turn 3/4. It is easy to get confused about how far to turn, so many people find it helpful to "count walls" as they turn.
It doesn't matter if the mini-wave is right-handed or left-handed. The dancers just hold hands and walk forward 3/4 of a circle around that spot. Some people find it helpful to mentally break this 3/4 down into 1/2 plus 1/4, and think about doing a Trade (Arm Turn 1/2) followed by a Hinge (Arm Turn 1/4).
As with Hinge, often more than one pair of dancers will be doing a Cast Off 3/4 at the same time. And as with Hinge, if dancers start facing head walls they will end facing side walls, and vice versa.
Cast Off 3/4 can also be done when the two dancers in the same half of a line form a couple (facing the same direction). In this case, they start turning away from the center of the line. Note that this is the opposite of the direction that they would start turning for a Bend the Line or a Wheel and Deal. They still turn, as a unit, a total of 3/4 (270 degrees). They will end facing the dancers from the other half of the original line.
From a line consisting of two couples facing the same direction -- i.e, where all four dancers are facing the same direction -- one of the couples will start turning to the left and the other will start turning to the right.
The same rule applies for a couple in any kind of line. In the case of a two-faced line, the couples will be turning in the same direction. For example, from a right-handed two-faced line, they will both be turning to the left, away from the center of the line.
But in either case they will be turning away from the other couple, and they will still end up facing the other couple. If you are in a couple, forming one half of a line, and after doing a Cast Off 3/4 you aren't facing the dancers from the other half of that line, then either you didn't turn 3/4 or you turned in the wrong direction!
Note: Some people think about the couples case of Cast Off 3/4 in terms of the center dancers "pushing" the couple around. For this reason, this case is traditionally referred to as a "push cast".