You can achieve what you described with the table model I gave you. As a general rule, you want to keep your tables in normal form. at least 2nd normal form, but the standard is 3rd normal form.
See http://www.phpbuilder.com/columns/barry20000731.php3?page=1 for a good, clear article on this. I think this will clear things up for you.
With one assignment that can be assigned to many sections, and one section being able to have several assignments, you have an M:N relationship. Sounds to me like you need an associative table:
you'll have 3 tables: assignments, sections, and section_assignments(section_id,assignment_id).
If an assignment goes for 3 sections (say the teacher can select several sections to be assign the assignment to from a mutiple select form item), you would have something liek this:
$insert1=mysql_query("insert into assignments .....your insert code");
$result=mysql_query("select LAST_INSERT_ID() as ID from assignments");
$assign_id=mysql_fetch_array($result['ID']);
(if the section selection comes from a multiple select menu, it will be returned as a comma-delimited list, so you must convert it to an array in php)
$section_array=explode(",",$menu_sections_list);
foreach($sections as $key=>$value) {
insert2=mysql_query("insert section_assignments (section_id,assignment_id)
values ('$value','$ID')");
}