Is "the hands" part of the verb to wash? The solution was "the baby is washing his hands"
Maybe rather 'the child'
How would you say 'She is washing the child?'
Perhaps, this would be "Yeye anaogesha (I think anamwogesha is correct because the object is an animate) mtoto." = She is bathing a/the baby. Because the verb "-oga" (to bathe, to take a bath, to take a shower) is derivated as causative verb. I think -nawa can be used to clean yourself (or to help children to clean their face and hands): "Mtoto ananawa mikono kabla ya kula." = The child is washing his hands before eating.
Here, an example of a web page in Swahili about "How to give bath to a new born" / "Jinsi ya kumuogesha mtoto mchanga" (I think this is literally "Ways of bathing a recently born baby"):
(As we can see in the Swahili text, the verb -osha is sometimes also used for washing the body parts of a baby, but this verb is mostly used for utensils and other things. On the other hand, the verb -oga indicates "bathing the entire body".)
An example using the prepositional verb (with the infix "mw", object agreement for singular person, and this would be used for animates), Swahili translation from French:
anamwogesha mtoto wake katika beseni kubwa la plastiki (elle lave son bébé dans une grande cuvette en plastique)
https://books.google.com.ar/books?isbn=2845867948 (Section 12 - Page 164)
And Swahili translation to French:
Mama anamwogesha mtoto wake (La mère donne un bain à l'enfant)
https://books.google.com.ar/books?isbn=2865370658 (Section 21 - Page 378)
Edit: I have edited the parenthesis about the prepositional verb. I have read a little more about this and I think the correct use would be with the object infix (anamwogesha or anamuogesha) when this refers to animates and/or definite nouns.
Wow what an answer ! I'm deeply in your debts ! Thanks for taking the time ! I will take some time to digest this properly ;D
It is "Anamwosha mtoto." -osha already is the applicative (the g of -ofa disappears in -osha)