I think the difference is that "hälft" is a noun and "halv" is an adjective.
So, you could say "Jag vill ha hälften av dina saker" (I want half of your things) or you could say "Jag är inte hälften av mannen som brukade jag vara" (I'm not half the man I used to be).
With halv, you can describe things such as "en halvmåne" (a half moon) or "jag är en halv man och ett halvt lejon" (I am half man and half lion), or "Det tar ett halvt år" (it takes half a year). In this case, "halv" is describing a moon, a man, a lion, and a year.
This is how it was explained to me elsewhere (not on Duolingo), so mods please correct me if I'm wrong! Tack!
I had a problem with audio on this one. I
m not sure if it is Duolingo audio, my computer or my ears but I played the sentence numerous times in slow time and at normal speed and all I could hear was HELSTAN for halften. It wasnt a word that I recognise so I thought, "new word," and put it in. Obviously wrong!