"Durante los dos últimos años"
Translation:During the last two years
It is 100 times less common in google searches than the way Duolingo does it. That does not mean your way is wrong but it might sound odd when compared to the most common way. My guess is most of the time duolingo is judging things like this on mere instinct.
It makes sense but it's not said that way. There's only one "last year:, so "two last years" is awkward. Changing the order makes the time duration "two years", and the "two years" in question are the last two years.
I think pasado translates to past. As for 'two last years' I think it would be understood.
In my opinion, the wording, during the two last years should not be considered incorrect.
When there is no context, "during the final two years" does not work because that means that no more years will occur. However, if you are talking of a duration of time that happened and ended in the past, then "during the final two years" does work. For example, "During the final two years of World War Two ... ."
If you mean "during" when you use the word "last," then, yes, "over the last two years" is correct.