Hello there. This looks like a coil balance assembly: specifically, it may be our 15-251 Single Support, though you'll need to remove the assembly from the window to confirm there is just one coil spring per each side of the window sash. If there's more than one spring, you'll need a different sized-support system; if in doubt, send us a picture of the whole assembly removed from the window to confirm.
This system typically uses our Series 160 Coil Balances, which are a 1/2" thick. Once you remove the assembly, measure the thickness of the coil spring to ensure this matches up.
For removal and replacement, there should be a cutout at the top of the window track that you can use to slide out the original assembly. This is also where you'd put in the new assembly. You'll also note a bracket at the top of the track, probably the same design as our 16-032 . This is what connects to the "T" end of the Series 160 spring. The spring anchors to this mounting clip and extends while the rest of the assembly slides down the track.
Let me know if you have any other questions.