Right-handed vs. left-handed
This can be determined by seeing whichever hand allows you to curl from the x-axis to the z-axis (aka travel counterclockwise) when you point your thumb along the z-axis.
Given only the x-axis and y-axis, you can also use this test to determine which direction the z-axis should be facing: there’s only two directions that are perpendicular to both axes, so try both hands and see which one allows you to curl CCW.