"The women like colorful umbrellas."
Translation:Alle donne piacciono gli ombrelli colorati.
In the English phrase, "The women like colourful umbrellas", "the women" is the subject (who does the action of liking) and "colourful umbrellas" is the direct object (what [or who] recieves the action; answers the who or whom part of the question).
In the Italian phrase, this changes. For the verb "piacere" the subject will not be the one liking, but the thing that is liked (ie. "gli ombrelli colorati"). "Piacere" is not "to like", but more like "to be liked", or "to please". Now, "le donne" in the Italian phrase is not the subject nor the direct object (it does not receive the action). It is the indirect object (to whom the action relates).
A more literal translation of "Alle donne piacciono gli ombrelli colorati" would be "The coloured umblellas are pleasing to the women". In that English phrase the subject is "the coloured umbrellas" and "the women" are to whom the umbrellas please. In Italian certain prepositions tend to be in front of indirect objects. "A" is always used before an indirect object noun ( http://italian.about.com/library/fare/blfare166a.htm ), and here it is used to mark the "indirect-object-ness" of "Le donne".
I don't know if I've explained myself correctly, but basically I think there are two difficult things here. "Piacere" does not work like "to like" (but rather in the oposite way). And here we have (I think) one of the first examples of indirect object in the phrases that Duolingo gives.
I'm in an Italian class and we would never say the sentence this way. We would either swap Le donne for the indirect object pronoun, making it "Gli piacciono gli ombrelli colorati." or, if le donne needed to be there, it would be "Gli ombrelli colorati piacciono alle donne." It's a small complaint, but when I fail a test for saying it in a completely correct way, Mi non piace!