So when does "com" mean "of" rather than "with?" Is this "colher com" just a common phrase for "spoon(ful) of" or does this usage occur in other situations as well? i.e. Can "com" be used with other nouns than "colher" to mean stuff like "a car-ful of teenagers?" Any native speakers have any answers?
A spoonful of rice shoud be translated as uma colher cheia de arroz. You should use "de" when the noun is preceded by a measure. "Um copo com água - Um copo cheio d'água"; "Um quilo de bananas"; "Um metro de fita". You're not wrong, it's just not accurately translated in DuoLingo.