Basically "Ea ne arată" is enough, where "ne" is the weak dative form of noi. However it is common in Romanian to reduplicate pronouns for extra emphasis, which is why the strong dative form "nouă" is added at the end, but it is optional and the sentence is still correct without it.
To lebo_bebo, I answer you here because your question was at the end of thread.
Your example "She show us nine new cars" can be translated "Ea ne arată (nouă) nouă mașini noi." That because the adjective must follow the plural form of "mașini". The first "nouă" is not necessary because you have already the previous pronoun "ne".
"Nouă" as adjective is for singular feminine nouns, like
- "mașină nouă"(new car),
- "rochie nouă"(new dress) or
- "față nouă"(new face).