I just got my answer ‘Duolingo is going to Wales’ shot down. Oh come on >_>
I reported a similar exercise earlier on. I did receive an email saying they accepted "Duolingo" for that one. :-) I reported this one as well.
They both mean 'Wales'. But they are not interchangeable in the sense that you can use whichever you want in any sentence. 'Gymru' is a mutation of 'Cymru'. As to when it mutates, well, I'm a mere beginner and there are about twelve pages of rules about mutation in my Welsh grammar book!
Cymru mutates softly to Gymru here because it follows the preposition "i" (meaning "to"). Cymru ----> i Gymru