Hi Marchi,

You'll want to work this piece with the Jacquard technique.

When working jacquard, you work with two colors and leave the yarn you don’t use on the back (inside) of the work. When it’s time to use it again, you pick up the yarn and carry it across the back (inside) of your work before making the next color change. Take into account that a color change always starts a stitch before. The strands that remain inside your crochetwork between color changes must be loose enough so that the fabric doesn't pucker.

I hope this helps!