Translation:You have been able to write two books.
I agree. I wrote "You have achieved to write two books" and Duolingo accepted that but I guess this translation is too literal and maybe not correct in english. "You have been able to write two books" seems more natural in english.
What about "you have succeeded to write two books" ???
The infinative "escribir" can take the -ing ending of English when it is not used as an active verb. For instance, "Writing is my favorite activity" would be translated as "Escribir es mi actividad favorita." In US English, it is not common to say "To write is my favorite activity," although it would be understood.
So, in theory, you could translate this as "You have achieved writing two books" although Duolingo does not currently accept it as an answer. (It has been reported.)
After reading all the comments (which I always do, often deciding not to post) I am stymied on why this issue has not been resolved. I believe You have achieved writing two books IS standard English and You have achieved to write two books IS NOT standard English. It would be nice to see glaring discrepancies corrected, less confusion and a consistent professional level achieved throughout. No pressure, but, two years?
So does lograr mean "be able to" or "manage to". The reason I ask is that in English if you said "They have managed to write two books" you're implying that you are surprised by it - you expected them not to. "They have been able to write two books" (the Duolingo translation) doesn't have that same meaning.
That is what I put and agree with everyone that it makes little sense but I think it makes as much (or as little) sense as "You have achieved to write two books," either you would be met with confused faces. This is just one of those examples you just have to cop a heart and move on, at least take solace in the fact you are probably never going to say this to anyone...ever :)