Translation:This year has three hundred and sixty-six days.
3 hundred and 66... is, unfortunately, a silliness the system does by itself and we do not have how to stop it. In general we do not use numbers. Some sentences are in both, English for Czech speakers and Czech for English speakers, courses. So you can land such a sentence learning either of these. If you are learning English, allowing you to type 366 is really not going to help you with numbers much. And the other way round. Also, a lot of people tend to go to the 'opposite' course to improve their language skills.
I found the "dnu" completely inaudible. I played it four of five times at both speeds and still could not hear it. I only got the answer right because I knew that it must be there. I frequently find the last word difficult to hear in the lessons but is the first occasion in which I could hear no sound whatever.
In your sentence “this year” really means “in this year,” even though English does not use a preposition here. I don't think that “tento rok” can be used with that meaning. In Czech I would say “v tomto roce” or, shortly, “letos.” (Czech even has a single word for “last year” = “loni.”)
BTW, I would never use abusive abbreviations in a public forum but then I am not an English native speaker… I feel that difference all the time.
Assuming what you wrote is a DL-proposed correction, I think the Czech team would need to see your exact sentence in order to tell you what might have been wrong with it, and why you got that weird "right" translation.
The "3 hundred 66" thing has to do with how the system handles numbers. It seems to like 1- and 2-digit numbers, but throws up its hands in despair when it encounters 3-digit numbers. Best (though annoying) to type it out if the number is over 99, or just cross your fingers and use the same weird format.