Hello there. If this is a Certainteed window, then you most likely have the 15-192 Pivot Shoe, which works with Series 170 and Series 171 Coil Balances. The video below goes into detail on these parts. Let me know if you have further questions.
See the video below. This shows how to remove a different coil balance system, but the principles should apply. Basically you're going to want to release the coil system and remove it from the cutout further up the window track. Take a look and let me know if you have further questions or concerns.
The pivot shoe is the 15-192; however, as you probably can tell the cam is different. Unfortunately your shoe's older nylon cam is no longer available. This may not make a difference; however to be safe, you may want to swap this cam out with the metal one in the newer shoe. This would ensure that the new shoes are compatible with your window's pivot bars (the metal pins in the corners of the sash that hook up with the shoes).
As far as the coils, the 15-192 uses Series 170 and Series 171 coil springs. The Series 170 is all you need if there is only one coil on each side of the window sash. If there is two, then the Series 171 is used as the second coil. It has a longer 'tongue' that lets it stack atop the Series 170 and attach to the 15-192. See the video I posted earlier for a visual explanation.
Replacement coil springs have spring weights, which designate the weight they can individually support. For the Certainteed coils, a stamp of '407' denotes a spring that can support 7 pounds. If there is only one coil per side, then a coil stamped '407' should be replaceable with the S170-407 7 pound spring. If there are two coils per side, and the second, 'taller' coil is also stamped 407, then use the S171-407 spring for that second coil. If not all the coils are stamped, or you're unsure how to proceed, give me the exact weight of the window sash that these coil springs support, and I can calculate the spring weights you need.
You're very welcome! Best of luck with this project and please feel free to reach out if we can be of any further assistance.