The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is:

Vowels: I (2), O (1), E (1), U (1), A (1) $$\implies$$ Number of distinct vowels = $$5$$ ($$\{\text{I, O, E, U, A}\}$$)

Consonants: N (3), C (2), S (1), Q (1), T (1), L (1) $$\implies$$ Number of distinct consonants = $$6$$ ($$\{\text{N, C, S, Q, T, L}\}$$)

Ways to choose 2 distinct vowels from 5:$$^5C_2 = \frac{5 \times 4}{2 \times 1} = 10$$
Ways to choose 2 distinct consonants from 6:$$^6C_2 = \frac{6 \times 5}{2 \times 1} = 15$$
The selected 4 letters can be arranged among themselves in $$4!$$ ways.
$$\text{Total Words} = {^5C_2} \times {^6C_2} \times 4!$$
$$\text{Total Words} = 10 \times 15 \times 24 = 150 \times 24 = 3600$$