I make the r and ø sound like french (danish r is a little bit different, more guttural). Then the "d" sound is a little bit more problematic. The most similar sound in english is the "th" sound as in "those". But if you want to sound more danish, you should separate the tongue from the teeth a bit and it will sound like you are throwing up, just like danish :)
It's just something you have to keep hearing over time. I have 2 friends who are Danish that begin speaking to each other in Dansk around me. To this day, 2.5 years later I now today just was able to say it correctly ONE TIME. Just have to get used to hearing them talking. I recommend using Forvo.com to hear actual Danish speakers pronounce the words. Duolingo saying them doesn't completely help.
is it possible to say huns instead of hendes or does the word not exist?
No, you can't, like how it's impossible to say "shis" instead of "her" in English. You just have to get used to exceptions like that, especially with pronouns.
Here's a link to the Tips and Notes for this lesson to help you study them:
Have fun learning!
"hendes" only translates to "hers" in situations where you would use the possessive pronouns "mine"/"yours"/"theirs"... instead of "my"/"your"/"their"... In English you use these when the object that the person possesses is not directly following the pronoun. In Danish the words are the same for both situations.
For example: "It is my/your/her elephant. The elephant is mine/yours/hendes." = "Det er min/din/hendes elefant. Elefanten er min/din/hendes".