Answer: C. The graph gives particle displacement along $y$ while the wave travels along $x$ therefore particle motion is perpendicular to the direction of travel. A wave that displaces particles of a cord is mechanical and requires a material medium, so it cannot propagate through a vacuum.

A: reads the horizontal position axis as the particle-motion direction and assumes the wave can travel without a medium.
B: reads the horizontal position axis as the particle-motion direction, giving parallel motion.
D: identifies the perpendicular motion correctly but mistakes a mechanical wave for one that can propagate through a vacuum.

Remember: mechanical waves require a medium; electromagnetic waves do not.