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.
KnittingHelp Queen Bee
"There is a vitality, a life force, an energy, a quickening that is translated through you into action, and because there is only one of you in all of time, this expression is unique. And if you block it, it will never exist through any other medium and it will be lost. The world will not have it. It is not your business to determine how good it is nor how valuable nor how it compares with other expressions. It is your business to keep it yours clearly and directly, to keep the channel open. You do not even have to believe in yourself or your work. You have to keep yourself open and aware to the urges that motivate you. Keep the channel open."
— Martha Graham