How many words of 4 letters can be formed from the word "MED

You cannot use a single step permutation here. You will need to first select and then arrange since selection will vary in each case.

We have 8 distinct letters: M, E, D, I, T, R, A, N

Then there are some repetitions: 3E, 2R, 2A, 2N

In how many ways can you make a 4 letter word?

Case 1: All different letters
From the 8 distinct letters, you choose 4 and arrange them.
= 8C4 * 4!

Case 2: 2 letters same, others different
For the 2 same letters, choose one from the 4 which are repeated in 4C1 ways. Then to choose 2 other letters, pick two from the rest 7 distinct letters in 7C2 ways. Then arrange them in 4!/2! ways (you divide by 2! because one letter is repeated)
= 4C1 * 7C2 * 4!/2!

Case 3: 2 letters same, 2 letters same
Choose 2 letters from the 4 which are repeated in 4C2 ways. Then arrange them in 4!/(2!*2!) ways (2 letters are repeated so you divide by 2! twice)
= 4C2 * 4!/(2!*2!)

Case 4: 3 letters same, fourth different
Only 'E' appears 3 times so E must be chosen. You can choose the fourth letter from the other 7 letters in 7C1 ways. Arrange them in 4!/3! ways
= 7C1 * 4!/3!

All four letters cannot be the same since no letter appears four times.

To get the final answer, we will need to add the result from all the cases. I wouldn't worry about doing it. This isn't a GMAT type question. Needs a long monotonous approach. GMAT questions can be solved quickly and usually have a trick. This question is useful only to help you understand the basics of permutation and combination.