Answers:
There are no words in the English language without vowels. You would not be able to pronounce them, since it is the vowel that requires you to open your mouth and let out the air.
There are a few sounds, NOT words, that have no vowels, like psst and grr, but that is onomatopoeia and not really words.
Surely you aren't saying that words with just the letter Y for a vowel are "without vowels?" Y, and sometimes W, and at least once N acts as a vowel in English words. If your teacher is telling you only A E I O U are vowels, s/he is completely wrong.
If your assignment was to find verbs using only the letter Y as a vowel, then that's something entirely different. Then you could have such verbs as fly, pry, cry, try, tryst, ply, fry, etc.
(FYI one of the words with W as a vowel is cwm, and the N word is nth.)
Hope this helped!
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