That video is the absolute worst way to do it and he makes it take 11 minutes for what should take 30 seconds. It’s 11 minutes of what not to do.
Make your circle. Center it with the alignment panel (make sure artboard is selected). Draw a single slot. Center it horizontally, and then move it to the top of your circle, overlapping as necessary. Make sure you’re in the mode where you can see extra info (I can’t remember what it’s called at the moment and I’m on my iPad). The shortcut is Cmd/Ctrl + U. This will allow you to see the center point of the circle when you get your cursor near it. Hit R to bring up the rotation tool. Option/alt + click on the center. This will be your center of rotation. Your cursor should snap a bit to it and I believe it’ll say Center and highlight the circle. A dialog box will pop up. Enter 360/the number of desired copies. Hit copy. That will close the dialog and give you a copy at the new angle. Hit Cmd/Ctrl + D to duplicate that transformation including the copy. Do it until your slots are complete. Group those and use them with the pathfinder palette to subtract them, or select it all and hit Shift + M to bring up the shape tool where you can Opt/Alt + click the shapes you want to subtract or Opt/Alt + click and drag through the things you want to subtract. It’s easier to drag the line through multiple things to subtract them, especially since you’ll likely have 3 things to subtract for each slot.
Pathfinder is the way to go if you understand it. I think you’ll want “Minus Front” but it’s hard to know without being in front of it and seeing the layer order.
If you need more help, or if my explanation is confusing let me know. My side gig is doing straight to the point After Effects tutorials for advanced users on YouTube. I’ve been using AI for nearly 20 years and I still use it daily, so if you need more help I have no problem recording a quick video. I have everything set up.