"저에게 편지를 쓸 것이에요?"
Translation:Will you write me a letter?
This whole section keeps using like a reflexive grammar rather than just using "(verb) (direct object) (preposition) (indirect object)"
Another example of a poor job by DuoLingo with the translation, needs to be much more flexible, 저에게 편지를 쓸 것이에요? Are you going to write me a letter? Sounds just about right to me... but no... the only answer acceptable is Will you write me a letter? This type of question needs revision and should allow for more flexibility
Keep in mind that this is still the Beta Version.
This means that they know that everything is not perfect yet, but they still allow people to use it, in order to report problems when they see them.
If you want absolutely no problems, wait until they release the definitive version.