Ok, I've made the video. Please keep in mind that I would probably categorize this technique as an intermediate skill. So it might be difficult for a beginner to grasp, or maybe even notice all the details.
I think I gave you a link to the manual section about Snapping earlier. And the very first part of the video, I circled the mouse (highlighted with large yellow circle) around the snap control bar. The way it's set up is what I find to be a good general configuration, for most things, and it also happens to be a good setup for this technique. But as you learn more and more about snapping, you'll find that you may need to re-configure it, sometimes, for every step you take, in a very complex file.
The video also introduces z-order, very briefly, and certainly not comprehensively. But for this process, the z-order is important.
I made the strokes wider and gave them all different colors, which will hopefully help you to follow what's happening....although even with wider strokes, it's still hard to see the z-order. But it's impossible to understand what's happening, if you use fills rather than strokes....so I used strokes with colors. But it's still very confusing in the way that the strokes have to be all on top of each other. You could do the 2 path operations separately, and not on top of each other. And with snapping, it should be fairly easy to put everything back together. But I still prefer to keep everything on top of each other, to maintain maximum precision. Maybe you would want to practice with the 2 duplicate sets separated, so you can see what's happening better?
Let's see, what else.... Oh, the video puts a small blue circle around the mouse when I click. But it doesn't show key shortcuts. Because the 2 duplicate sets of objects are on top of each other, you can't use a selection box to select one of each. So I use the Shift key, to make a multiple selection (circle and rectangle selected at the same time). Also for key shortcuts, I hold the Shift key while clicking on a color chip in the palette, to color the strokes,
After I do the first Cut Path operation, you can see where I delete the top-left corner of the green rectangle. And then after that, I join the remaining 2 sections of the green rectangle. For that, you can see that I used the Node tool, and how I used a tiny selection box to select the 2 nodes which are precisely on top of each other. And the next step after that, I deleted that node. For that, I help down the Ctrl key, to make sure that part of the rectangle path stayed precisely straight. (Inkscape will make a curve by default, if there is even a 0.001 px distortion, so Ctrl keeps it perfectly straight.)
And then after I finished the 2nd operation, and deleted the unwanted parts of the circle, I also joined nodes of the green rectangle and red arc from the circle, using the same technique as with the rectangle.
If you have any question, just ask. I know it's a tricky technique for a beginner, and every single little step is important.
