"The ducks are my ducks."
Translation:Ördekler benim ördeklerim.
Because, otherwise it becomes an awkward sentence: "ördekler ördeklerim." It feels like you're repeating the same word twice, and the suffix at the end is too faint by itself in a sentence where the main objective is to let the listener know that something belongs to you.
You could omit "benim" in sentences where there is something else going on and the fact that a particular object is "yours" is of secondary importance. For example: "Ördeklerim uçabiliyor." (My ducks can fly.) Here, you're not drawing the listeners' attention to the fact that those are your ducks, but rather that they can fly. But if you also feel like stressing the fact that they're yours, you can include "benim" (Benim ördeklerim uçabiliyor. → MY ducks can fly.)
Why not "Ördekleri benim ördeklerim"? I know "i" means THE. Is this right?
Please learn the following rule. NO ACCUSATIVE ON THE SUBJECT. No matter if it's "the" or "a/an". Only the object of the sentence can be in the accusative.
Accusative for nouns ending in a consonant (like ördekler) looks the same as the 3rd person possessive. So, it's especially dangerous in this case as it would be understood as "His/her ducks are my ducks."
Hmm, I am interested that you go to see that alternative! :)
-DIr is used to state encyclopedic facts and strong assumptions. It is sometimes used in simple sentences (but it is better to assume that it is not used like this normally).