"Я не хочу с ними идти."
Translation:I do not want to go with them.
In Russian, After a preposition, the pronouns starting with a vowel take a "н" at the beginning. e.g. Его > за него, из него, и... Её > за неё, из неё Ими > под ними, с ними Их > за них, из них И тому подобное (= etc.)
This only happens with pronouns starting with a vowel. (so they can be distinguished more easily in speech) The pronouns (его, её, их, ему, ей, им, ими....) take the "jumpy" "н" because they start with a vowel.
Why is "I don't wanna go with them" not accepted? "don't" instead of "do not" is accepted, so why not "wanna" instead of "want to"?
Wanna is not a contraction of want to in the same way that don't is a contraction of do not. Instead, wanna is a slang spelling of admittedly unorthodox pronunciation - it comes from running words together. Because of the effort required to form the sequential "-t t-" sounds in want to, we instead remove the t's and convert the elongated ooh of to to a shortened uh.
However, even those of us who are lazy about pronouncing want to will still spell it out in full when we are writing. Granted, you will see wanna in written form, but it is generally used in very informal communications, like in text messaging or in social media, or in quoted representations of idiomatic speech. Such quoted representations highlight that the person being quoted is not speaking formally, or perhaps is speaking impolitely.
"Do you want to go with me to get a snack?" she asked the boy.
"I don't wanna," he growled. "I wanna play with my toys and watch TV."
Wanna has become, at least in my area, almost unnoticeable in spoken English, though I have noticed that some people will say wannoo, which still loses the "-t t-" but does not sound quite as potentially impolite as wanna.
So wanna really should not be accepted as a standard answer from Duo. I hope this helps!
It's so informal as to be unacceptable in many written situations. This may change with time. A descriptivist would call this correct, in that it's easily understood, means what you want it to, and is naturally generated by native speakers. Flag it and see what happens.