Question

How much energy does the electron have initially in the n=4 excited state?what is the change in energy if the electron from part a now drops to the ground state?

Answer 1

What it looks to be that you found in A was the "initial"...b/c the question asks: 
"how much energy does the electron have 'initially' in the n=4 excited state?" 

"final" would be where it 'finally' ends up at, ie. its last stop...as for this question...the 'ground state' as in its lowest energy level. 

The answer comes to: −1.36×10^−19 J


You use the same equation for the second part as for part a. 
just have to subract the 2 as in the only diff for part 2 is that you use 1squared rather than 4squared & subract "final -initial" & you should get -2.05*10^-18 as your answer.