"They live on the island for years."
Translation:Ele trăiesc de ani de zile pe insulă.
Sometimes in Romanian we say ani de zile or luni de zile instead of just ani or luni.
If it would have been They live on the island for months. you could translate it as Ele traiesc de luni pe insula. but it wouldn't be clear whether you're saying months or Monday, and we would probably assume it is Monday.
So my guess is that in order to make it clear we are talking about months, we say luni de zile and it perhaps got transfered to ani de zile too without any benefit that I can think of.
Thanks to Lurch for noting I posted in the wrong place. Post copied here for convenience: The proposition does not require the definite article (which is implied), unless the noun is qualified eg by an adjective (so the translation of eg "on the big Island" would have required the "insula" form.