Which is not a medium through which a mechanical wave could travel?

liquid water

jump rope

oxygen gas

empty space

Mechanical Wave cannot travel in space vaccumes, which would be considered "Empty Space" in your situation.

A mechanical cannot travel through empty space. So option (d) is correct.

A mechanical wave is a wave which needs a material medium for its propagation. For example sound, water waves etc. The medium required by the wave can be a solid, liquid or a gas. Empty space doesn't have any medium, so a mechanical wave cannot travel through empty space.