Quilt each nine-patch to the towel backing it with the stitch-in-the-ditch method: sew down all the long seams, following the seam lines that you made when you pieced them.
At this point, I’m going to cheat: if you’ve never sewn anything that needs to be sewn wrong sides together and turned right-side-out through an unsewn opening that is then top-stitched closed, please turn to my stenciled bean bags tutorial, in which I show you step-by-step how to do exactly that. The only difference is that with a potholder as opposed to a bean bag, you lose the fuss of trying to keep those dried beans in as you sew, but gain the fuss of sewing through fabric that is thick, thick, THICK! Clip your corners well, trim your seams close to the stitching, use a heavy-duty sharp needle and a relatively long stitch, and sew slowly, and soon you’ll have the Tardis blue and Captain Picard’s uniform red nine-patch potholders that you’ve long been dreaming of.
Loved your simple but excellent idea for potholders. I’m gonna whip some up for myself and even make some for next year’s Christmas so, for a change, I’m ahead of the game. Instructions are well written, nicely illustrated and fun, as always.