Thanks for reaching out! Your coil balance assembly reminds me of our Series 220 Roller-Tilt assembly. I noticed that your base is stamped with a 6, however, we only have the S220-08 8lb base available. The good news is that you can use the S180-4 along with the 15-086 Tandem coil housing to get you to the 12lbs you need for both sides of the window. So the balance assembly will still be able to support a 24lb sash.
Carefully review the dimensions for the Series 220 to confirm that it will be a fit.
Let me know if you have any questions.
The part you are searching for is what is called a mounting clip. There are three compatible with the type of coil balance assembly you have. So to determine the clip needed for your window, you'll need to compare them to your existing hardware.
Take a look at parts 16-030, 16-031, and 16-036. See which of these is the best fit for your window.