Alternate approach, solve using example.
For n=2 and there are 2n people = 4
Consider that the four people are {M1, M2, F1, F2} – M stands for male and F stands for Female.
Now, let's count the number of good parties. Considering that k is the number of males or females.
for k=0, number of good parties = {} = 1
for k=1, number of good parties = {M1, F1}, {M1, F2}, {M2, F1}, {M2, F2} = 4
for k=2, number of good parties = {M1, M2, F1, F2} = 1
total number of good parties = 1 + 4 + 1 = 6
Comparing against the answers derived from options
option 1 = 2^n = 4 is incorrect
option 2 = n^2 = 4 is incorrect
option 3 = (n choose n/2)^2 = 4 is incorrect
option 4 = (2n choose n) = 6 is correct
Ans: D