Hints:

1. Concentrate on the region of space to the right of the oscillating charge.
2. Watch the electric field lines, and observe the "wave" created, which moves along the positive y direction (from left to right in the region to the right of the charge).
3. As the charge moves upward, what is the direction of the current produced? What, then, is the direction of the magnetic field to the right of the charge? (Remember the right-hand rule.)
4. As the charge moves back downward, what is the direction of the current produced? What, then, is the direction of the magnetic field to the right of the charge?
5. Along what direction (x, y or z), then, does the magnetic field oscillate?
6. In what direction do you see the wave moving?
7. What, then, is the relationship between the directions of the oscillating E and B fields and the direction of propagation of the wave?

Reference

See Walker, Section 25-1

Illustration written by Steve Mellema