"Obrigado" and "Obrigada" means the same, "Thank you". But if you are a man, you should always say "Obrigado", and if you are a woman, always say "Obrigada".

Somewhere the difference between "obrigado" and "obrigada" should be made clear.

At the moment, it seems Duolingo has an issue with "Obrigado vs Obrigada". It says that "Obrigada" = "Thanks" whereas "Obrigado" = "Thank you". If you answer anything different from that, you get a wrong answer...

"Obrigado" and "Obrigada" are the same thing and both mean "Thanks", with the difference being that men always say "Obrigado" and women always say "Obrigada", regardless of the gender of the person they are talking to.

Yes, it should. http://duolingo.com/#/comment/60688