Looking at the original drawing, arrange the stripes onto the background. You can line the stripes up perfectly according to my drawing, but you will soon realize that if you want the whole background to be covered, you are going to have to shift and blend the stripes so they didn't look like perfect repeats. Hey- mother nature isn't perfect, and niether are my zebra stripes. Just have fun with the placement.
Go a little crazy and switch up the colors on the outer edges of the fat quarters. When everything looks good, fused it all down. Then sew the two chunks together. Notice, I offset the background seams to add interest.