var checkbox = document.getElementsByName("likes[]"); 
//此处通过此种方式才能获得多选框为数组。
                                            
//like为name = "like[]" , 获得时必须加上[]
var checked_counts = 0;

for(var i=0;i<checkbox.length;i++){
if(checkbox[i].checked){     //被选中的checkbox
checked_counts++;
}
}

alert(checked_counts);

function checkDate(){ 
  var n = $("#cart_q_num").val(); 
   var checkedCount=0; 
   var checkbox = document.getElementsByName("tie_in[]");
   //alert(checkbox.length);
   for(var i=0;i<checkbox.length ;i ++){ 
   if(checkbox[i].checked){ 
     checkedCount++; 

     } 
   } 
   //alert(checkedCount);
    if(checkedCount>n){ 
       alert("The quantity of the gifts should equal to the quantity of the sunglasses set."); 
      return false; 
   }else{
     $("#free_pro_selected_num").html(checkedCount);
    }
}

<input type="checkbox" name="tie_in[]" value="1" onClick="return checkData()" />