"Cups and plates are on the shelf."
Translation:Чашки і тарілки на полиці.
І, й and та are equivalent grammatically, you can use either one, they are all OK and all will be accepted on Duo too.
In spoken language people seldom pay attention which one they use. As a general rule, use them freely based on your feeling and aesthetic preferences.
In written language, in important speeches, theater, in more "literary" occasions they are used depending on the words before and after "and" to create a melodic sound. General rules are, priority #1: avoid two vowels in a row, priority #2: avoid two consonants in a row.
Let's say we want to say X and Y.
Case 1: X ends with a consonant, Y begins with a consonant --> use і (кіт і пес)
Case 2: X ends with a vowel, Y begins with a vowel --> use й (Аня й Оксана)
Case 3: X ends with a vowel, Y begins with a consonant --> use та (мама та Марія)
Case 4: X ends with a consonant, Y begins with a vowel --> use й; the general rules above tell us that "saving the vowels" has more priority, therefore we prefer "Дід й Оксана" to "Дід і Оксана".
As I said, in daily life nobody does this with conscious effort really, it happens naturally. It depends on your own preference. If you feel like "Дід й Оксана" sounds ugly or is not easy to pronounce, you say "Дід і Оксана" or even "Дід та Оксана" even though the last one is breaking all the rules :) Sometimes following the rules actually makes it less melodic! E.g. "Я у школі" (I'm at school) would sound horrible if you said "Я в школі" (three consonants in a row + not easy to pronounce).
Duolingo (as well as spoken language) accepts all these interchangeably and rightly so :)
P.S. I don't know other languages doing this kind of stuff apart from Italian: tu ed io VS io e tu (you and me, me and you), a Roma VS ad Alba (in Rome, in Alba)