Answer
There exists one plane determined by AB and DC.
Work Step by Step
Imagine the figure as a box of tissues. The plane defined by segments AB and DC would be one side of the tissue box.
If you need, gab a tissue box (or any other box) and label each corner with the points shown in the picture. You will easily be able to determine the six planes that make up the 'outside' of the tissue box. (Note: There are a few more planes that can be found by slicing 'through' the tissue box, intersecting any three vertices of the box.)
