"The woman eats rice."
Translation:Η γυναίκα τρώει ρύζι.
No, rice in Greek is ρύζι or in uppercase ΡΥΖΙ. NOTE it is Ζζ not Ξξ nor Χχ.
I think you will like these links which show the Greek letters and their English equivalents. There are some other also useful links.
And here is another to help you navigate Duolingo
FAQ - General Questions, Bugs Reports
Some simple rules to get you started:
Always read the comments before posting.
Read the Tips notes right below the list of lessons on your Homepage
Read the drop down hints. Pass your cursor over a word and a list of words will appear.
That is the correct pronunciation for "γυναίκα". If you check the links shown just above yours you will see among others a list shown the approximate pronunciation of each letter.
E.g. Γ-γ Γάμμα (Γάμα) //Gama|γ |as in game or yes
There are also links to sites it native speakers to access.