You now have finished the seams of the gusset for the purse and the purse lining.
You can use thread, perle cotton, etc to attach your hinge to the purse...match the color of thread to your fabric if you do this. Or you can using clear filament (fishing line) which is what I'm going to use here. This is a 6lb test weight line. Begin by tying a knot in your thread and needle up through the purse from the lining side at the TOP CENTER point through the center top hole in the clasp. Then needle down into the next hole (on either side) and continue this needle-up/needle-down in subsequent holes until you reach the edge of the clasp (hinge area) as shown in the above photo. This cause a series of RUNNING Stitches to form along the hinge...and through the outer/lining fabrics. Work to keep the purse fabrics pushed into the hinge a you stitch.
Now, reverse and stitch in the same manner until you reach the center point of the hinge again. This covers 1/4th of the hinge in secure stitches. Repeat this for the opposite side of this same hinge side. End again at the center.
OPTIONAL: Repeat this process for decoration purposes...by adding beads as you repeat the stitching. Work your needle back through previous holes or previous beads to completely fill the space with beads.
End your thread by taking a couple of tiny slip stitches into the hinge area of fabric, and knot off the thread. Repeat the process of attaching the hinge on the opposite side of the hinge in the same manner at for this first side.
Hope you will be inspired to create your own hinge purse soon!