it sounds like "he opens my wallet"
It can also be understood like that, because besides being a reflexive pronoun, "mình" can also be understood as first person singular pronoun ("I"), usually used among peers.
thank you huy =)
Why is there no classifier before ví here?
I asked myself the same question, because we speak about a specific wallet (his own)
Anh ấy mở [cái/chiếc] ví [tiền] của mình
 = optional
That's why I like vietnamese, so flexible :-) even more than chinese
I ask the same question re classifier for a specific noun. Mr/Ms Yu's explanation below is not to be found
because of the possessive của following the noun, as Huy explained here: https://forum.duolingo.com/comment/34006704/I-find-her-wallet