Pivot Lock Shoe
Hello! Your pivot shoe appears to be a good match for our 15-188. However I would recommend reviewing our dimensions to ensure that they all line up.
The metal cam in your shoe is currently pointed up, making a "U" shape. That means it's locked in place. What you need to do is take a flat head screwdriver and turn that so that it's a "C" shape, then gently allow it to rise up towards the balance until the balance cord is fully retracted.
It's very important to keep a firm grip on the screwdriver when you unlock the shoe. It's under a lot of tension from the balance, so when it's unlocked it's going to try to shoot up into the frame. You have to let it slowly rise back up, otherwise you could do permanent damage to the window.
Once the shoe is up, simply disconnect the balance from the shoe and remove it from the window. That will give you the clearance you need to slide the shoe all the way up to the take-out slot at the top of the track for removal.
If the metal cam is broken then it may be trickier to remove than usual, but the same principles still apply. You may just need to get creative in terms of how you guide it up the track, depending on just how significant the damage is.
I need 4 of them.
That does appear very similar to our 15-188, yes. Size is unfortunately not something I can determine from a photo of a tape measure. Your next step should be to review the dimensions I shared for it above to confirm that they are in alignment. Note that width and thickness are the most important details. Height is not that important.