Best way to combine ring and delete excess?

Trying to make the above example for my project on the bottom. Any clue how to go about keeping the ring in the box and removing the out of the box part of the ring?

Boolean operations or Clip Content in a frame.

  1. Intersect selection with the ring and box selected
  2. Create a mask with the ring and box
  3. Create a frame that is the same size as the box, put the ring inside and tick “Clip content”. I think this is the most straightforward for your case.

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