Hello there!
Thanks for reaching out to us. This looks like the 15-197 shoe. To remove old shoe from balance, place the channel balance in a vice and with a pair of pliers, pull the broken piece about 12" from the balance and lock it with a pair of locking pliers, taking the tension off the old shoe and giving you some slack with the balance string. Either untie the old shoe or cut the knot off to remove the old shoe and install the new shoe. To install the balance into the window, remove sash, screw or hook channel balance on the top of the window jamb. With a pair of pliers, pull down the shoe, about 12", and lock the string with a pair of locking pliers. With the tension off you can install the shoe into the window track.
If you aren't handy, we recommend consulting a local professional for assistance.