Ответ:

  1. Give me another peach, please.
  2. One is ours, the other is our neighbour’s.
  3. Would you like another cup of tea?
  4. Look! Your cousin is on the other side of the street.
  5. Try on another dress.
  6. We never see the other side of the moon.
  7. One was quite easy but the other problem was rather difficult.
  8. Give me another pen, please.
  9. One is my brother and the other is his best friend.
  10. I’d like to watch another film.
  11. She had a cake in one hand and the flowers in the other.

Правило: another употребляется в значении «ещё один/другой» перед существительным в единственном числе; the other — «другой из двух» или «оставшийся».