If each word is only 4 letters, then no word can have more than two vowels, and words with 2 vowels are limited in their permutations.

For this, we would need to find the total number of permutations that are possible if we had only 2 letter words containing only vowels. Then we would have to multiply this by the total number of permutations that can exist of two letter words that contain only consonants. Note also that such combinations of consonants and vowles have only 2 possible arrangments: (v)(c)(v)(c) or (c)(v)(c)(v). For this reason, we would multiply the above product by 2.

Next, words containing 1 vowel need to be done in a similar process: We would need to find the total number of permutations of 1 letter words containing only vowles. Then we would need to multiply this by the total number of permutations of 3 letter words containing only consonants. Notice that this combination of 3 consonants and 1 vowel, has for arrangments: (v)(c)(c)(c), (c)(v)(c)(c), (c)(c)(v)(c), (c)(c)(c)(v). Therefore, we would need to multiply the above result by 4.

Last, words containing no vowels are the easiest to compute. We need only find the total number of permutations of 4 letter words containing only consonants.

Finally, we add the totals from each step to find the total number of possibilities.