Translation:Can you explain to me why you do not like him?
It has to do with nitpicky grammar on the English side. The idea is that if you break the sentence up into 2 pieces, "can you explain to me" and "why you don't like him," only one needs to be posited as a question (the first half). "Why don't you like him" has the word order of a question, so this answer (although colloquially fine and should be accepted) has the form of a question within a question, instead of a subordinate clause ("why you don't like him").
It is not two separate questions "Can you explain to me? Why do you not like him?".
Instead, "why you do not like him" is part of the main sentence -- it acts almost like a noun, the object of "explain".
Indirect questions such as that one have a different word order in English from direct questions (that are sentences of their own).
So it has to be "Can you explain to me why you do not like him?", without a comma and with "...you do..." rather than "...do you...".
Yes. With "explain" you need "to" there.
Don't ask me why, but so did many native speakers tell me in another topic :) Although some said, they would consider it to be ok, but still they would prefer the "to" version.
But in this sentence the reason is kind of clear: "Explain me" could also be a question to ask someone to explain you as a person, not to explain to you.
Generally the rules whether to use "to me" or just "me" after the verb say, that you should use it only when there cannot be ambiguity.
There is some flexibility with the word order of this sentence, but unfortunately, you can't change it to be what you wrote. Wieso in this sentence acts as a subordinating conjunction, which forces the predicate verb (mögen/magst) to go to the end of the sentence. '
Since German word order places the more important info towards the end of the sentence, it becomes an issue of meaning/emphasis of du vs. ihn.
Kannst du mir erklären, wieso du ihn nicht magst -- this sounds more natural to me, because the point of the question is asking why you don't like HIM; i.e. what's wrong with him
Kannst du mir erklären, wieso ihn du nicht magst -- this could also work, but is less organic and would have to be super situational, since you would emphasize DU; i.e. everyone likes him, why don't you?
Why do you think ihnen would be correct?
That's dative plural ("[to] them") -- but mögen is a normal transitive verb, and so it takes a direct object in the accusative case. Dative would make no sense here.
So what you are hearing must be ihn -- masculine accusative ("him").
Nobody can see what you wrote, so references such as "this" or "my answer" or "the translation" are not helpful.
If you have a question why something was not accepted, please always quote your entire answer -- with copy-and-paste if possible, rather than re-typing it.
Even better: take a screenshot that shows the question and your answer, upload it to a website somewhere (e.g. imgur), and tell us the URL to the image.