Translation:¿Por qué no se lavan ustedes la cara?
I think it's because in English we say "faces" because we're talking to at least two people, so we see at least two faces.
In Spanish we say "cara" because each person has only one face
The "se" comes before the "lavan". The rule for object pronouns (direct objects, indirect objects, reflexives) is that they have to go immediately before a conjugated verb.
If your sentence contains an additional verb form, like an infinitive or a present participle, then you have the choice to put the object pronoun before the conjugated verb or attached to the end of the infinitive or the present participle.
Se lavan la cara. (only a conjugated verb = only before)
Se van a lavar la cara. OR Van a lavarse la cara. (conjugated + infinitive = choice)
Se están lavando la cara. OR Están lavándose la cara. (Conjugated + present participle = choice)
Reflexive verbs usually use definite articles with parts of the body and clothing.
He washes his car. Él lava su carro.
He washes his face. Él se lava la cara.
See my response to lunzie about "caras."
Is there a reason for the location of ustedes in this sentence? Does anywhere else work?
This seems like a question parents might ask their children, so could it not also be correctly translated as "¿Por qué no os laváis la cara?"