inkscape - How to remove the part of a shape that is not within the rectangle?

How can I keep just the part of the shape that is inside the rectangle?

I would like to do something like this:

Here's the original video I've seen this from: (StackExchange doesn't allow me to post more than 2 links, so I'll put the link in a comment to this question).

What is the technique used by the designer to keep just the part of the circles that are within the rectangles? I tried slowing the video down to 0.25, and all I've seen is that he went to the Path section, but I don't know what he clicked on.

Here's my "remake"

As you can see from my "remake", the circle is above the rectangle, but I can't hide the part that is not within the rectangle.