"Do you like my plates?"
Translation:Placentne tibi patellae meae?
However, if using "-ne" as a question-marker, you want to put it at the beginning of the sentence.
This is often done, as Duolingo does, by putting it on the verb and starting with the verb: "Placentne ... ?"
It can be attached to other words ("Itane... ?" = "Like this ... ?", "Tune ... ?" = "Are you really ... ?" / "Did you really ...?"), but putting it first is necessary, otherwise the interlocutor doesn't get the message soon enough, that you're asking a question.
I wrote "Tibine placent patellae meae?"
I know that it's more common to have the -ne on the verb, and the first word, but as -ne is used to ask a yes/no question about the word where it's placet. And because I read some examples in Latin literature and grammar books, my sentence is also correct, and would mean:
Do you like my plates (is it really "you" that like my plates)?
Because the -ne is on "tibi".
The same way, I could chose to write uncommon, emphatic sentence like:
"Meaene platelae tibi placent?", putting the emphasis on "meae" (really mine, not someone's else.)
I know it changes the meaning, and that is not the common, usual way.
If you need an authority for this (we are studying Latin, after all) you can find it in question 332.a of Dickinson College Commentaries (http://dcc.dickinson.edu/grammar/latin/questions)
"The interrogatives particle "-ne" is sometimes omitted.
Patēre tua cōnsilia nōn sentis? ( Cat 1.1)
Do you not see that your schemes are manifest (you do not, eh?)
Note - In such cases, as no sign of interrogation appears, it is often doubtful whether the sentence is a question or an ironical statement.
Why is it tibi, the dative
You can think of placere as meaning "be appealing, appeal".
So if you like the plates, then they appeal "to you".
If you speak other languages, compare also Spanish gustar, French plaîre, Italian piacere, and German gefallen, all of which put the experiencer in the dative case or equivalent (preposition a, à).
(The French and Italian are derived from placere, of course.)