I guess you are having dropdown with values 1,2,3 etc which is ID Column.,
In your dropdown selected index changed event,
Write a new sql command to update
SqlCommand cmd=new SqlCommand("update tbl set Date=@Date where Id=@Id",connection1);
cmd.Parameters.AddWithValue("@Date",DateTime.Now);
cmd.Parameters.AddWithValue("@Id",Convert.ToInt32(cmb.SelectedValue.ToString()));
connection1.Open();
cmd.ExecuteNonquery();
connection1.Close();