"I do not paint chairs."
Translation:Nem festek székeket.
I'm still working this out, but I think that nem had to immediately precede the word it negates, in this case festék.
However I'd like to know if "székeket nem festék" is wrong or whether it needs to be reported.
You have a typo. "Festék", with an "é", is a noun meaning "paint". The paint that you buy in the store.
What you need is "festek", which means "I paint". A verb in the first person singular.
Other than that "Székeket nem festek" is also perfectly fine. The relation between "nem" and "festek" remained the same, you only moved the object in the front, making it more emphasized.