This should get you working.
<%# ((DataItemIndex % 4 == 0 || DataItemIndex % 4 == 1) ? "<div class='large-6 small-6 columns topicTxt'><div class='article-block' onclick='location.href='" + GetDocumentUrl() + "' style='cursor:pointer'><em class='author'>" + Eval("Author") + "</em><h4 class='title'>" + Eval("Headline") + "</h4>" : "<div class='topicFoot'><span class='topicIcon " + Eval("Specie") + "'></span><span class='topicPlay'></span><span class='topicLink'></span></div>") %>Remember if you are already inside a code block (<%# %>), you don't need to put another code block around an Eval("Name") again, I think that is where you're problem came from. Easiest thing to do is create them in Visual Studio to help get the syntax part correct, then paste into the text editor on the site and see how it looks.