Hello, thank you for taking the time to post your question!
In order to solve this one I think it wants you to use the formula
Number of spectral lines = n*(n - 1)/2, where n is the initial principal quantum number (meaning the shell the electron is in)
In this case since n = 4 is given in the question the calculation should be
4*(4 – 1)/2
=4*3/2
=12/2
=6
So the maximum number of different spectral lines possible is 6
I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)