Duolingo should really fix all the sentences using "가는 길". It makes just as much sense in english to say "The road going home." Why not use that as the reference sentence so we don't all get it wrong the first time?
There are actually 2 movies and a series.
집으로 (가는 길) 2002 with young 유승호. A very touching and warm hearted movie.
집으로 가는 길 2013. A tragedy based on a true story.
집으로 가는 길 2009 Romantic family (very long) dorama.