Pass your function name at anchor tag, your function name is " delete_activity_edit " and you call " edit_activity ".
<a href="http://localhost/weekly_report/activity/delete_activity_edit/172"></a>
then check if it will enters in delete_activity_edit function using echo. Like this;
public function delete_activity_edit()
{
$id=$this->uri->segment(3);
echo $id; exit;
$this->activity->remove($id);
redirect('activity/edit_activity/');
}
then check if it enters into function, it will the 3rd segment value i.e. 172. After that remove 'echo' and 'exit ' and check if record deleted successfully.
Using redirect('activity/edit_activity/'); you will redirect to edit_activity function of activity controller.