Word order query
Why is it l’année dernier but mes dernieres années? What’s the rule?
Last year is a fact and an analytical, literal use of the adjective, but "my last years" is subjective. This reminds me of "Mes vertes années" which means "my productive years" another subjective use of an adjective which is very different from the literal use of the adjective. Also in English, "green years" would not mean the same thing. The subjective version of the adjective used in an expression comes before the noun.
Scroll all the way down at this site: https://www.thoughtco.com/introduction-to-french-adjectives-1368789
In this particular case, the adjective meaning is not too different, but I tend to look up any adjectives before nouns as sometimes the meaning is very different. http://dictionary.reverso.net/french-english/
There is also the difference between an and année: https://www.thoughtco.com/an-annee-jour-journee-matin-matinee-1371085
http://www.dummies.com/languages/french/how-to-place-of-french-adjectives-correctly/ Take a look at these sentences from that last site: "Le dernier jour de la semaine est dimanche." The final day of the week is Sunday. In English, we could also use the word "last", but there is a difference in meaning from "Dimanche dernier, il a fait des crêpes." "Last Sunday, he made pancakes." "Last Sunday" means the one before now (previous), the most recent past one, rather than the final one.
So then, how do we know that these are my final years, what if I live longer? I am still talking after all? This is obviously an expression, not much we can do about that, except learn it. It does fit into the view of being subjective though. Maybe, I think I will die soon.
Think of "un grand homme" which is "a great man" vs. "un homme grand" which is "a tall man". Whether a man is great or not is subjective, while whether he is tall is something you can see.