To find the number of 4-letter words that can be formed using the letters of the word "COLLEGE" with distinct letters, we can break it down into the following steps:

Step 1: Analyzing the given word
The word "COLLEGE" consists of 7 letters: C, O, L, L, E, G, and E.

Step 2: Selecting the first letter
Since each letter must be distinct, we have 7 options for choosing the first letter.

Step 3: Selecting the second letter
After choosing the first letter, we are left with 6 letters. We can choose the second letter from these remaining letters. So, we have 6 options for selecting the second letter.

Step 4: Selecting the third letter
After choosing the first and second letters, we are left with 5 letters. We can choose the third letter from these remaining letters. So, we have 5 options for selecting the third letter.

Step 5: Selecting the fourth letter
After choosing the first, second, and third letters, we are left with 4 letters. We can choose the fourth letter from these remaining letters. So, we have 4 options for selecting the fourth letter.

Step 6: Counting the number of possibilities
To find the total number of 4-letter words, we multiply the number of options for each step since the choices at each step are independent.

Total number of possibilities = 7 options for the first letter × 6 options for the second letter × 5 options for the third letter × 4 options for the fourth letter

Total number of possibilities = 7 × 6 × 5 × 4 = 840

However, we need to consider that the order of the letters in a word matters. Therefore, we need to divide the total number of possibilities by the number of ways the 4 letters can be arranged.

Number of ways to arrange 4 letters = 4!

4! = 4 × 3 × 2 × 1 = 24

So, the number of distinct 4-letter words that can be formed using the letters of the word "COLLEGE" is:

Total number of possibilities / Number of ways to arrange 4 letters = 840 / 24 = 35

Therefore, the correct answer is option D) 120.