But why is NAAE 1?

since N and E is fixed and the two letters between is A, there is only one way to form this 4 letter code

Ahhh thank you!!

… agree with part (i) answer, but I believe that part (ii) answer should be 270.

… for arrangement with double A,
there are still 4 different letters remaining
(counting 2 same Ns as 1 letter).
4C2 ways to select 2 letters from 4. therefore,
no. of ways = 4C2 x 4!/2! = 72

… similarly for arrangements with double N,
no. of ways = 4C2 x 4!/2! = 72

total no. of ways = 6 + 72 + 72 + 120 = 270.

… and you did remember to multiply the 5C4 for last case of all letters different . . . . . . hmmmm