"He reads her a magazine."
Translation:Él le lee una revista.
Because he reads 'to her', he doesn't read her. I had the same problem, found this helped: http://spanish.about.com/cs/grammar/a/objectpronouns.htm
I'm unclear as to why you would not add "a ella" to the end of the sentence making it: "El le lee una revista a ella." Just two sentences before this one I correctly translated "He writes her a book" to "El le escribe un libro a ella." Why is "He reads her a magazine" translated as "El le lee una revista" instead of "El le lee una revista a ella?"