Tampoco means "neither", or "not ... either" (DuoLingo is misleading by showing "either" as an option)
So you can use "neither" or you can use "not ... either", replacing the "..." with the clause that follows "tampoco" in Spanish.
Often when I am translating an unfamiliar sentence structure, I try word-for-word first, and then rearrange it to make it sound like correct English. So "Eso tampoco es una naranja" = (word-for-word) "This neither is an orange", or "This not (is an orange) either". Not particularly nice sentences in English, but they give an idea of what the sentence means, and by simply swapping "not" and "is" gives "This is not an orange either".
"¿Eso es una naranja?" is the correct way to phrase the question (Is that an orange?).
The dialogue might go something like...
Juan (pointing at an apple): ¿Eso es una naranja?
Maria: No, eso no es una naranja.
Juan (pointing at a peach): ¿Eso es una naranja?
Maria: Eso tampoco es una naranja.
Gracias! Your explanations on this thread are very good, especially pointing out the misleading duoLingo translation and explaining the use of negatives in Spanish. In Maria's last reply, would it be incorrect to add a "No," at the beginning of the sentence? "No, eso tampoco es una naranja."
I agree that including "either" as a translation can be misleading, but you can't just translate one word at a time.
You need to remember that Spanish has a different way of expressing negatives to English, so you need to understand how words like "tampoco" and "nunca" work.
E.g. "No es una naranja tampoco" = "It is not an orange either".
See how in this almost word for word translation "tampoco" does get translated as "either", and in fact saying "It is not an orange neither" would be considered bad English.
Another example with "nunca" (which means "never") --- "¿No vas nunca al cine?" = "Don't you ever go to the cinema?".
Notice that even though, "nunca" is "never" we translate it as "ever" here. It comes down to understanding how Spanish uses negatives together, whereas English does not.
because when it's in a sentence with what we in English call a "double negative" we have to sometimes translate it as "either" because of the English grammar.
Un virus no es un animal. Ni una planta tampoco. My Spanish grammar may be incorrect, but the idea I'm getting at is we can translate this into English as "A virus is not an animal. Nor is it a plant." or we could say "It's not a plant either." or "It's also not a plant."
I'm open to correction ...