The textbook acknowledges that it is difficult for students to hear the difference between /y/ and /ø/ in Danish.  So they provide a list of words to listen to.  However, the authors are not taking into account that Danish spelling does not reflect Danish pronunciation! (You could have told them that, eh?)  Below, I've rearranged the list given in the book so that words with the same sound are grouped together under the International Phonetic Alphabet (IPA) symbol for that sound.  The small diacritic that looks like a question mark without a dot (  ) is the symbol for a glottal stop, and the colon (:) means that the preceding vowel is long).  Anything between slashes (/ /) indicates a sound, and anything italicized means spelling.  A word with the same letter may have different sounds when it appears in different words!  Your job? Compare and contrast, listen and repeat at will!