It seems that "The hat is purple" is a correct translation, but "The hat is mauve" is not. However, "The cap is mauve" is marked as correct. This seems like an oversight.
I wrote "The hat is mauve" and it was wrong. "Right" answer: "The cap is mauve"
Mauve is not a common word, for ESL (non-native english speakers) it's confusing (most of them even being level C1 haven't even heard it). I suggest to use only purple.
For a native British English speaker mauve and purple are completely different, it's almost, but not quite the same relationship that pink has to red. Purple and mauve should really not be substituted for each other
The instruction was to type what I hear. This is what I wrote: Το καπέλο είναι μοβ. It was marked incorrect and the answer given was exactly what I wrote. I am using an iPhone 6s and working from the website. I took a screenshot, but was unable to post it to this compose window.
The best thing to is file a bug report here https://support.duolingo.com/hc/en-us/requests/new. Include as much information as possible, as you have done in your comment, and attach the screenshot.