Question

What set of rotations would carry parallelogram ABCD onto itself?

Answer 1

Do not know if you have a set of choices for the answer, because there are many ways to rotate the parallelogram, depending on the centre of rotation.
Rotations about any point through 360 degrees will carry the parallelogram onto itself. However, if the centre of rotation is positioned at the intersection of diagonals, a 180 degree rotation will give the same parallelogram, but the labels (letters) will be "inverted".