To find the number of different words that can be formed with the letters of the word EQUATION without changing the relative order of the vowels and consonants, we need to consider the arrangement of the vowels and consonants separately.

1. Arrangement of Vowels:
The word EQUATION has 4 vowels - E, U, A, and I. To find the number of arrangements of these vowels, we treat them as indistinguishable because we cannot change their relative order. This can be calculated using the concept of permutations of indistinguishable items.

There are 4 vowels, so the number of arrangements is given by 4!.

2. Arrangement of Consonants:
The word EQUATION has 3 consonants - Q, T, and N. Similar to the arrangement of vowels, we treat these consonants as indistinguishable and calculate the number of arrangements using permutations of indistinguishable items.

There are 3 consonants, so the number of arrangements is given by 3!.

3. Total Arrangements:
To find the total number of different words, we multiply the number of arrangements of vowels by the number of arrangements of consonants since the arrangements of vowels and consonants are independent of each other.

Total arrangements = (number of vowel arrangements) * (number of consonant arrangements)
= 4! * 3!

Calculating the values,
4! = 4 x 3 x 2 x 1 = 24
3! = 3 x 2 x 1 = 6

Total arrangements = 24 * 6
= 144

Therefore, the number of different words that can be formed with the letters of the word EQUATION without changing the relative order of the vowels and consonants is 144.

However, none of the given options match with the correct answer of 144. Therefore, none of the provided options is correct for this question.