If the four letter words (need not to be meaningful) are to be formed using the letters from the word "MEDITERRANEAN" such that the first letter is R and the fourth letter is E, then the total number of all such words is:

First letter is R and Fourth letter is E.
So now we have 11 letters left with 2E, 2A, 1M, 1D, 1I, 1T, 1R and 2N.
And with this we have to form a two-letter word.
There will be 2 cases when both these two letters of the middle will be the same. And this will be when they both are either EE, AA or NN.
Now when middle two letters are not same. So we have to form a 2 letter word with 8 letters without repetition .
Number of such words will be 8 × 7 = 56
Hence, the total number of such four-letter words with R as the first letter and E as the last letter will be 56 + 3 = 59.