@AFulgens: That's only the description. If our woman check the taste and if the taste of the soup is fine we will answer: "DER Frau schmeckt die Suppe" and not "Die Frau schmeckt die Suppe". Its Dativ with the word "Wem" schmeckt die Suppe? Answer: Der Frau schmeckt die Suppe.
Otherwise, if Duolingo will use "Die Frau" it's only correct, if the woman is cooking a soup, make salt and pepper inside and checked the soup. That's in english not taste, but rather season to taste. Then we use the verbs "abschmecken", "probieren" or "verkosten", but not "schmecken".
The right terms are: "Der Frau schmeckt die Suppe" or "Die Frau schmeckt die Suppe ab".
Maybe the problem is to search for a direct translation in english. That is not my first language so i can't really check it. Maybe taste or tasty can be, and reading your link my conclusion is this verb is about to the "flavour" but not with the action of "try". but how i said maybe the problem is "try" in english has more exceptions and without the appropriate context is difficult. A last note, in real life with germans speakers, they use this verb after you have eat the food to check if you like it. But i'm just a begginer so maybe i'm wrong ^^
So in one case "schmecken" works like "gustar" in Spanish, where the person is the indirect object, not the subject? Should I see it then as two homonym verbs: Schmecken (like: person is indirect object, thing is subject), Schmecken (taste: person is subject, thing is direct object).