it's more or less like German ö or French œ.
You start by pronuncing the o of English "boy" then you push your lips forward as if you were going to give a kiss.
Do it in front of a mirror and after a few tries it will work.
Børn and bjorne sound very similar in this audio. Taken out of context and given Duolingo nonsensical phrases, this is a poor example. Hope to learn but this is frustrating.