"The way home is long."

Translation: La vojo hejmen estas longa.

[Mr.Knight]

Why does "hejme" take the accusative -n in this case?

[Kivolamuzikisto]

It's the "accusative of motion" used to show that's it's the "way TO home" (homeward). There's more in this thread:

https://forum.duolingo.com/comment/8853203/Kial-vi-iras-hejmen

[n2fole00]

Why is home an adverb here?

[TheSnowKing]

It means "homeward", that is "toward home".