The number of words that can be formed with the letters of the word 'DEFINITE' if two vowels are together and the other two are also together but separated from the first two is

DEFINITE has 8 letters: Consonants: D, F, N, T (4 distinct); Vowels: E, E, I, I (4 letters with repetition).

The condition requires two groups of 2 vowels each, separated by at least one consonant.

Arrange 4 consonants: $4! = 24$ ways, creating 5 gaps: $\_C\_C\_C\_C\_$

Choose 2 gaps (separated) for the two vowel groups: $\binom{5}{2} = 10$ ways

Arrange 4 vowels (E, E, I, I) in the 4 slots: $\dfrac{4!}{2! \cdot 2!} = \dfrac{24}{4} = 6$ ways

Total $= 24 \times 10 \times 6 = 1440$