Transverse and longitudinal waves are two categories of waves that differ from one another in terms of how the particles of the medium vibrate. In a transverse wave, particles of the medium vibrate perpendicular to the medium. In a longitudinal wave, particles of the medium vibrate parallel to the medium. These different particle vibrations result in different-looking wave patterns. This is discussed in detail in the How to Think About This Situation section below.
 

As a longitudinal wave moves through a Slinky, the coils of the Slinky vibrate back and forth about a fixed position known as the resting position. The direction of the particle motion is parallel (and anti-parallel) to the Slinky. At any given moment in time, there will be regions along the Slinky where the coils are pressed together very closely. These regions of maximum closeness are known as compressions. There are also regions where the Slinky coils are spread apart with a maximum separation distance. These regions are called rarefactions.

In this question, you will notice that there are no crests and troughs. There are only compressions and rarefactions. So you know this is a longitudinal wave. And because it is a longitudinal wave, you know that the coils of the Slinky are vibrating parallel to the Slinky.