The number of 4 -letter words, with or without meaning, each...

The given word is INCONSEQUENTIAL.

The vowels present in the word are I, O, E, U, A. There are $5$ distinct vowels.

The consonants present in the word are N, C, S, Q, T, L. There are $6$ distinct consonants.

We need to form $4$-letter words consisting of $2$ vowels and $2$ consonants without repeating any letter. This means all $4$ letters in the formed word must be distinct.

Number of ways to select $2$ distinct vowels from $5$ distinct vowels = $^{5}C_{2} = \dfrac{5 \times 4}{2} = 10$

Number of ways to select $2$ distinct consonants from $6$ distinct consonants = $^{6}C_{2} = \dfrac{6 \times 5}{2} = 15$

Number of ways to arrange the $4$ selected letters = $4! = 24$

Total number of $4$-letter words that can be formed = $10 \times 15 \times 24 = 3600$

Answer: $3600$