Answer
Six transitions are possible.
The six possibilities are, listed by initial and final quantum levels:
4 to 3 (lowest-frequency light produced because this is the smallest energy drop)
4 to 2
4 to 1 (highest-frequency light produced because this is the largest energy drop)
3 to 2
3 to 1
2 to 1
Work Step by Step
For photons, E = hf, where E is the energy, h is Planck's constant, and f is the photon's vibrational frequency.