"What is on the plate?"

Translation: Mi van a tányéron?

[Arcaeca]

"tányéron" is some weird exception to the rule of vowel harmony, I guess?

[vvsey]

I don't know the exact rule but it is not just about the last vowel that counts. The description of the whole phenomenon is longer than one would think.

Here, "tányér" has mixed vowels, and is a simple word (not a compound word). So it gets the "low" vowel suffix.

[RyagonIV]

What I have seen when I learned a lot of words is that it happens quite often with words that have é next to back vowels. Acél, árnyék, tányér, béka, and répa currently come to mind. (Seems mostly to befall words with a or á. Hmm.)
I suspect there was some old phonetical thing there that classified as a back-vowel sound which now only exists as é anymore. That might also explain why there's no back-vowel counterpart to -ért, and maybe the strange behaviour of the conditional, first person singular indefinite (tartanék - I would hold).

[Tusy22]

You are getting there. But i í e and é were all back vowels a long time ago. So that is the reason you do not see ö ő ü ű in mixed vowel words. That could also explain férfi - férfiak, híd - hidat, cél - célok.
What you say about -ért is correct.
The conditional first person singular is -nék, but you would not know if you listened to some Hungarian speakers, -nák everywhere, it just hurts my ears.
Hope I helped.

[Tusy22]

Note to what I added. There could be ö ő ü ű in mixed vowel words but those are compound words e.g. hajmeresztő.

[vvsey]

Also, "-nák" has another role. It is the third person plural definite suffix.

tartanák - They would hold (it)

[Tusy22]

Sure it does, you're right. Though I was talking about the first person singular. That's why I said it hurts my ears. Foreigners who bother to learn Hungarian always get it right, it's my fellow natives who struggle with this.

[Tusy22]

I wish it was that simple. I've looked on different websites, but some of them just make it even more complicated. The link I'm supplying here is quite good, especially because it gives examples, so even if you do not understand all of it, you have a chance of getting it right.

https://sites.google.com/site/tanuljmagyarul20091113/home/gramatiko/vokalharmonio