You should set up value for your options, like this:
<option value="Engineering" name = "departments">Engineering</option>
<option value="Marketing" name = "departments">Marketing</option>
...
Than in your PHP put this:
$subject = $_POST['departments'];
This isnt best solution but it will work.
Better would be to define somewhere in PHP file (config) array with available departments $departments = array(1 => 'department1', 2 => 'department2')
, in html template make foreach loop above array of departments set value to key in array and in email script use $deparments[intval($_POST['departments'])]