"We wash ourselves."
The second "nos" in your translation needs a macron on the o to be considered accusative. If this is not what makes the translation correct in duolingo's eyes, it must be a discrepancy. Note that the second "nos" you have used in your translation is entirely unneeded and efficiency could be a possible practice duolingo is trying to nod you in the direction of. In normal Latin conversation, your translation would sound most cumbersome to someone hearing you say it.
Thank you, Zach-sensei. When I came up with my answer, I had the SOV word order in mind, while I imagine OSV might be possible. Do you mean the object by "the second 'nos'"? Either way, a quick lookup of nos in the dictiobary suggests that the vowel is long for both nominative and accusative. Though not expressing the pronominal subject overtly may be possible and more common, I chose to write my sentence for practice, having seen Duo's own: Ego me lavo .