program work06;
var n,y,r:integer;
begin
write('please input the year');readln(n);
write('please input the month');readln(y);
case r of
  1,3,5,7,8,10,12: r:=31;
  4,6,9,11: r:=30;
  2:begin
     if (n mod 4=0) then begin
       if (n mod 100=0)then
         begin
           if (n mod 400=0)then
              begin
                r:=31;
              end
           else
              begin
                r:=30;
              end;
         end
       else
         begin
           r:=31;
         end;
      end
     else begin
           r:=30;
          end;
   else writeln('WRONG!');
  end;
writeln('there are',r,'days in this month');
readln;
end.

拜托

2月，平年是28天，润年是29天。而不是30或31天……

program work06;
var n,y,r:integer;
begin
write('please input the year');readln(n);
write('please input the month');readln(y);
case r of
  1,3,5,7,8,10,12: r:=31;
  4,6,9,11: r:=30;
  2:begin
     if (n mod 4=0) then begin
       if (n mod 100=0)then
         begin
           if (n mod 400=0)then
              begin
                r:=29;
              end
           else
              begin
                r:=28;
              end;
         end
       else
         begin
           r:=29;
         end;
      end
     else begin
           r:=28;
          end;
   else writeln('WRONG!');
  end;
writeln('there are',r,'days in this month');
readln;
end.
改过了，可是还是提示“error in statement”

write('please input the year');readln(n);
write('please input the month');readln(y);
case r of

需要判断的是年份，并据以为月份 r 赋值，而你判断的是什么？你的 r 似乎还没有赋值，能不错吗？

最简单的方法是直接将 r 也一并输出，调试无误后再按实际需要修改。