Your hello class has a property mobilenumbers but the code is using mobile so it won't even compile, I assume this is a typo? Where you try and add the mobile number if you use the debugger you'll see that obj.mobilenumbers is null so you can't call any methods on it like "add". Objects like Lists etc only exist when you create them, so you need to create the list before you use it
string user = (string)Tempdata["user"]
var result =db.tblname.Where(em=>em.name==user).ToList()
list<hello> lst = new list<hello>;
foreach(var item in result)
{
hello obj = new hello();
obj.mobilenumbers = new List<string>();
obj.name = item.name;
var mobile = db.tblmobile.where(em=>em.name==item.name).ToList();
foreach(var item1 in mobile)
{
obj.mobilenumbers.Add(item1.mobile);
}
}