The number of six letter words (with or without meaning), formed...

Given word 'VOWELS'

Number of words Arranging all the letters $= 6 !$

In the given word Consonants are W, L, S.

Treating all the consonants as one unit then number of units will be $4 .$

No of such arrangements $= 4 ! . \left(3 !\right)$

VOWELS all the consonants never come together =Total - all consonants come together $= 6 ! - 4 ! \times 3 ! = 576$