Breakdown of Könnt ihr euch die Hände waschen?
ihr
you (informal plural)
euch
you (plural, informal)
können
can / to be able to
waschen
to wash
Questions & Answers about Könnt ihr euch die Hände waschen?
Why do we use euch die instead of just saying eure (your)?
In German, when doing something to your own body parts, you usually don't use possessive words like eure (your). Instead, you use a reflexive pronoun like euch to show who the action is happening to, followed by a simple definite article (die) for the body part. It literally translates to "Can you wash the hands for yourselves?".
Is euch in the dative or accusative case here?
It is in the dative case! The direct object of the sentence (the thing being washed) is die Hände, so that takes the accusative slot. Because the accusative spot is already filled, the reflexive pronoun indicating "to yourselves" must be dative. For the pronoun ihr, the dative and accusative forms both happen to be euch, but it is grammatically dative in this sentence.
How would this sentence change if I were asking just one friend?
If you are talking to one person using du, the sentence becomes Kannst du dir die Hände waschen?. The modal verb changes to match du, and the reflexive pronoun changes to the dative form dir.
Why does waschen go at the very end of the sentence?
This is because of the modal verb könnt (can). In German, a modal verb pushes the main action verb (waschen) to the very end of the sentence in its infinitive (unchanged) form. The modal verb itself sits at the front because this is a yes/no question.