Solution: Baffling Bands
The strip of paper is cut as shown in three places. The paper is then twisted and joined together so that the letters match A to A and B to B. This creates the first band.
The second band is created in a similar way, with two sets of cuts instead of one. The cuts are done opposite, and the paper is simply twisted two times so that the letters match up.
The second part of the challenge is to create the shapes from the first part by starting with uncut bands of paper. This is accomplished by taping the bands together with a twist (or two) already in them. When the cuts are made (the same way they are in the first section) the strip will untwist itself to form the bands.