When the girl generates a wave on the rope, we clearly see that it advances forward, towards the tree. So, the direction of wave movement is either to the left or to the right depending on where the tree is located.
Under this scenario, when we see how the rope moves, we see that it moves in up/down direction as the wave pulse passes. Since the up/down direction is perpendicular to the right/left direction, we conclude that the particles that make up the rope move perpendicularly to the direction of wave movement. Hence, we know that it is an example of a Transverse Wave.
