In English would you say "the cat washed nothing yesterday"? You could but you would probably say "the cat didn't wash anything yesterday". As you continue studying you'll learn that the word nada can be used this way, it makes no sense to those of us who speak English as a first language so we just have to learn it.
Maybe it has something to do with, let's see, the use of the past tense (of levar, in this case) --- or maybe the Spanish use of double negatives? Does it really matter whether it's the cat who didn't wash anything, or the boy, or the grandma, or the doctor? (Oh, wait. I guess it would matter if el doctor no lavó nada.)