Where is the accusative case in this sentence? Μου is a genitive and το πουκάμισο is a nominative, as it is the subject of the verb. The presence of this sentence in this section, without further explanation (which is not possible because that's not how Duolingo works) is at best misleading. I'd recommend removing it.
to πουκάμισο is neuter.
To πουκάμισο in accusative case is same as in nominative case.
But in this sentence, το πουκάμισο is in the nominative case, as the subject of the verb αρέσω (to appeal) -- the shirt appeals to me, μου αρέσει το πουκάμισο = I like the shirt.
if I put ‘μου’ at the end of the sentence. i.e “το πουκάμισο αρέσει μου’´
That's not possible -- short-form pronouns such as μου always come before the verb.
So you can have Το πουκάμισο μου αρέσει or Μου αρέσει το πουκάμισο but not Το πουκάμισο αρέσει μου.
If you want to put "to me" after "appeals", you need the long-form pronoun and an explicit preposition "to": Το πουκάμισο αρέσει σ' εμένα.