Consider the four letter as
E _ _ R

We are asked to fill the remaining two letters. Since E & R has already been picked form MEDITERRANEAN what remains is
M D I T R EE AA NN
So we have to pick 2 letters out of 11. But the important thing here is that E , A & N are repeated.
So we have 8 unique letters and 3 repeated letters in the remaining 11. The 2 numbers can be selected in the following 2 ways:
1) Both are different : first letter can be selected out of 8 & second one from remaining 7. = 8*7 = 56 ways.
2) Both letters are same: There are on three combinations AA, EE & NN = 3 ways
So total numbers of possibilities = 56 + 3 = 59

What's the OA?

The word starts with E and ends with N

E _ _ N

We have 8 unique letters in the word. We already have used two[E and N]. So we have 6 letters for remaining two places.

6 x 5 = 30 possibilities.

Is it correct? What is OA?

How many different four letter words can be formed (the words need not be meaningful) using the letters of the word "MEDITERRANEAN" such that the first letter is E and the last letter is R?

now simple condition E_ _ R
now there are two case
1st case

when repetaion is not allowed E _ _ R
1 2 3 4 (position of blank)
as letter need to be start by E so 1 st position can be filled in 1 way
as there are 13 letter in that word second position can be filled in 6 ways ( there are only 8 distinct letter and E has occupied first place and R occupies last place )
since repeatation not allowed of of letter 3 rd place can be filled in 5 ways (as 2 letter occupie first place)
as word need to end with R 4 th place can be filled in 1 way
so total number of word formed 6*5=30

second case ) repeatation is allowed
when repetaion is allowed E _ _ R
1 2 3 4
as letter need to be start by E so 1 st position can be filled in 1 way
as there are 13 letter in that word second position can be filled in 13 ways
since nothing said about repeatation of letter even 3 rd place can be filled in 13 ways
as word need to end with R 4 th place can be filled in 1 way
so total number of word formed 1*13*13*1 =169
check OA to find out what is asked i guess if not given anythin we go for repeatation

Total number of posssibilities = 56 + 3 = 59