The correct table is the third one:
Property Does a mechanical wave possess this property?
- They can be transverse. Yes
- They can be longitudinal. Yes
- They can propagate in a vacuum. No
- They can propagate in a physical medium. Yes
- They are composed of high energy particles. No
- They transfer energy from particle to particle. Yes
This table accurately describes mechanical waves: they can be both transverse and longitudinal, cannot propagate in a vacuum, must propagate through a medium, are not composed of high energy particles, and transfer energy through interactions between particles.