"He likes studying."
Translation:Του αρέσει να μελετά.
I've got the sense that διαβάζω, σπουδάζω, μελετάω, μαθαίνω have slightly different meanings, but I'm not quite sure I've fully got to grips with them yet. σπουδάζω, I think, implies higher education study, with the other 3 being a bit more general. But I could be wrong...
I agree. Σπουδάζω would be higher education study (σπουδάζει στο πανεπιστήμιο, σπουδάζει φυσική etc.); διαβάζω would be the act of studying for school at home (or in the library etc); μελετάω would be a more intense version of διαβάζω, implying serious concentration/effort (it can also mean to study/research/scrutinize/analyse: ο ποιητής μελετάει τη συμπεριφορά τον ανθρώπων - the poet studies people's behavior); μαθαίνω would be simply learning something (new), e.g. ο γιος μου μαθαίνει να διαβάζει - my son is learning to read.
Because the way to say 'somebody likes something' in Greek is like saying 'something is pleasing to somebody', with the whole subject-verb-object structure inversed.
Therefore, studying=να μελετά becomes the subject of the verb and he becomes the object αυτού. Another way to write it is Σε αυτόν αρέσει να μελετά, using the (σε+) accusative for the object, but you can use the pronoun in the genitive form before the verb, just like you could use the weak form του (Του αρέσει να μελετά).
Του αρέσει να αυτός μελετά is wrong because αυτός is wrong in this structure. The only thing that can come between να and a verb is the negative particle for the subjunctive μη(ν). You cannot put a pronoun right before the verb in the subjunctive.
Αυτού αρέσει να μελετά is not accepted because we say Του αρέσει... or Σε αυτόν αρέσει...
I appreciate JacobPast177's explanation of the near synonyms, but maybe Duolingo could get the question and hints to agree on which of the synonyms they want. It's a bit unfair to the student when the only hint for a brand new word (το διάβασμα) is an entirely different word than any of the available answer tiles (να μελετά or another conjugated form of μελετάω that is now covered by the answer banner, so I can't see exactly what it was). At least include the desired answer among the hints.
This is on the Android app, if the behavior differs between platforms.
Του αρέσει να μελετά = He likes studying
Να μελετά του αρέσει = Studying is what he likes (not something else). Completely different inflection, not wrong, but not what the original sentence says either. Just because Greek syntax is more flexible it doesn't mean that you can switch things around and get the same result. :) It's generally best to stick as close to the original as possible, unless there's a good grammatical reason to adopt a new structure in the translated sentence.