Hi. I wanted to make a suggestion regarding the Duolingo interface. Along with the answer, there should be a "view explanation" button which gives a short but useful description of the new concept in the sentence. E.g. the above sentence would have the explanation: "eto becomes etu when placed next to devochku".
If you say Он знает твою девочку, it follows the same rule as эту. It is linked to the word next to it.
But without ever seeing it in the course, you would maybe never know that твоя becomes твою (tvoy"U"), or that эта becomes эту in the accusative case. They could have precise it in the notes of the course, but it may be more effective to let you meet this situation and figure out yourself at the moment (if you think enough).