If that is correct, the answer is:
Because, there are just there are only six different letters.
Frankly I find the next three parts very poorly put.
I can help with part e. Consider three cases: no repeated letters (part a), exactly one pair of repeated, and two pairs of repeats.
Exactly one pair of repeated: . Select the repeated one from three. Then select two from the other five to be different. Now arrange these.
Two pairs of repeated letters: .
Now add those three numbers to answer part (e).
How many numbers can be formed using all of the digits 1, 2, 3, 4, 5, 6, and 7 if the odd digits must be in ascending order and the even digits in descending order?
There are seven places. Choose four to put the odd digits in ascending order.
Put the three even digits in the remaining spaces in descending order.
So the answer is .