documentclass[10pt,a4paper]{article}
usepackage{tikz}
usepackage{pgfplots}
usepgfplotslibrary{groupplots}
begin{document}
begin{figure}
  begin{tikzpicture}
     begin{groupplot}[
         group style={group size=2 by 2},
         cycle multiindex* list = {very thicknextlist rednextlist
         only
         marksnextlist}
     ]
     nextgroupplot addplot {x}; addplot {x^2};
     nextgroupplot[cycle list = {red, blue}] addplot {x}; addplot
     {x^2};
     nextgroupplot addplot[green] {x}; addplot {x^2};
     nextgrouplot %Here I am not sure what to do
        begin{groupplot}[
                            group style={group size=2 by 2},
                            cycle multiindex* list = {very
                            thicknextlist rednextlist only
                           marksnextlist}
                           ]
           nextgroupplot addplot {x}; addplot {x^2};
           nextgroupplot addplot {x}; addplot {x^2};
           nextgroupplot addplot {x}; addplot {x^2};
           nextgroupplot addplot {x}; addplot {x^2};
       end{groupplot}
     end{groupplot}
   end{tikzpicture}
 end{figure}
end{document}