So actually, for Japan, this English isn’t that bad. Japanese people just don’t get the difference between “together” and “with you.” (Or you could change the subject to “we”.) The actual Japanese, よんでる？, is a very colloquial way to say “You reading?”. I assume what they wanted to get across with the English is, “Let’s read books!”
Really, what pains me the most about this poster, as you might be able to tell by the bottom, is that this is–in all likelihood–a government sanctioned poster by the school library association. Yes, I took this picture at one of my schools. Yes, they are therefore tacitly approving of incorrect English in schools. Yes, I’m the only one who finds this strange.
Please keep in mind that I totally support reading. But I particularly like reading when it utilizes correct grammar.