The given sentence includes NO indication of whose legs and feet are being washed, so it is wrong of Duolingo to require us to assume "his" when it is not stated.
When it is not stated, then it refers to the person mentioned in the sentence.
It "might" be, but that is too specific and not quite natural English.
In Portuguese, when something obviously belongs to someone, we don't really need the possessives.
Body parts and clothes are the best candidates.
Mas... Se você NÃO disser "suas", são as pernas de quem?!?
But ... If you DO NOT say "your", are the legs of who?!?
When the possessive adjetive is not included, it refers to the subject of the sentence. If you say "ele lava as suas pernas e pés", the first thing that will come to a native speaker's mind is "He washes your legs and feet".
I assumed that he washes just legs and feet, not his, ie. his child, and that was incorrect answer
I'm not sure, but I guess that "He washes legs and feet" would be "Ela lava pernas e pés." Maybe he's a nurse working in a hospital so he's washing legs and feet.