It looks like you're supposed to follow the instructions as for the headband, which says to carry both colors at once, knitting in color A, then purling in color B, across the row; and on the reverse side, knitting B and purling A.
Your project is a very simple form of double knitting, in that the colors don't cross from front to back. One color stays on the front, and the other on the back. So the two sides are not connected except at the side seams.
You can work it as instructed, or you can cheat in this case. There are two ways to cheat, which avoid having to carry both yarns across every row:
Knit the front piece seperately. Then knit the back. Sew them together along all sides.
Or...and this is another method of double knitting....
Knit the first stitch in color A, bring the yarn to the front and slip color B p-wise, bring the yarn to the back to continue; repeat across the row. On reverse rows, Knit in color B, yarn forward, slip color A, yarn back. Be sure to twist yarns together at side edges, or you can purl the last stitch of each row with both colors and slip the first stitch of the row, to join the yarns neatly.