A hydrogen electron is elevated from level 1 to level 2. Another electron is elevated from level 2 to level 4. The transition requiring the greatest energy change is level 1 to level 2level 2 to level 4both require the same amount of energy

Think of energy levels in a hydrogen atom like a very strange set of stairs. The steps (E levels) are widely spaced at the bottom (require big steps). When you climb to the top, steps are closer (lower difference in energy). So a 1 - - > 2 transition is going to be bigger than the two steps in the 2 - - > 4 transition, but you could calculate it by using the Rydberg equation.

E for 1 - - > 2 transition is: 1.6x10^-18 J

E for the 2 - - > 4 transition is: 4.1x10^-19 J

(So the 1 to 2 transition is ~4 times bigger in terms of energy!)