Okay, click on one of the white lozenges to select it, then Right Click on it and choose Release Clipping Mask.
Do that for all four lozenges and you’ll get something that looks like this:
The lozenges appear to be a black stroke shape with no fill on top of a white filled shape with no stroke. I’m not sure if you intended to set up a separate score there or not, but when we use the shape subtraction tools it’s best to do it with fills only. From an engraving standpoint, it’s what you want to do, and if you need to create a cutline instead, you create it using the final subtracted result.
So if you don’t want to keep the scores, go ahead and click on the black lines and delete them. Be careful not to select the white filled shape inside.
One last step, select the white lozenges and the black outside octagon at the same time, and click on the Minus Front tool in the Pathfinder palette.
That will remove the overlap areas from the octagon underneath. If you want to create a cutline there, give it a stroke color.
That took a little longer than expected due to the duplicated lozenge shapes - it’s really not a difficult process.