Identify the letters in UNIVERSE

The word UNIVERSE has 8 letters: $U, N, I, V, E, R, S, E$

Since the letter $E$ is repeated, the distinct letters available are: $U, N, I, V, E, R, S$

Classify vowels and consonants

Vowels among these are: $U, I, E$ So, number of distinct vowels $=3$.

Consonants are: $N, V, R, S$ So, number of distinct consonants $=4$.

Choose 2 vowels and 2 consonants

Number of ways to choose 2 vowels from 3: $\binom{3}{2}=3$

Number of ways to choose 2 consonants from 4: $\binom{4}{2}=6$

Hence, total selections of letters: $3 \times 6 = 18$

Arrange the 4 chosen letters

All chosen letters are distinct, so the number of 4-letter arrangements is: $4! = 24$

Total number of words

$18 \times 24 = 432$

Final answer

The required number of 4-letter words is: $\boxed{432}$

Comparison with stored answer

Stored correct answer = $432$.

Our derived answer also equals $432$, so it matches.