The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is ______.

We need to form 4-letter words from the letters of UNIVERSE with exactly 2 vowels and 2 consonants, without repetition.

First, note that the vowels are U, I, E, E (with E appearing twice), while the consonants are N, V, R, S and are all distinct.

When selecting 2 vowels, there are two possibilities. Both vowels could be distinct, which gives $$\binom{3}{2} = 3$$ ways to choose from {U, I, E}, or they could both be E (using both E’s), which gives 1 way.

Choosing 2 consonants from the set {N, V, R, S} can be done in $$\binom{4}{2} = 6$$ ways.

After selecting the letters, we arrange the 4 chosen letters. If all four letters are distinct, there are $$4! = 24$$ arrangements. If the multiset contains two E’s and two distinct consonants, there are $$\dfrac{4!}{2!} = 12$$ arrangements.

Combining these cases leads to the total count:

The answer is $$504$$.