You'll need to add the user that runs the web server to the sudoers file first.
Something like this - replace www-data
with the user that runs the web server
www-data ALL=(ALL) NOPASSWD:/sbin/tc qdisc del root dev eth0
That will let the www-data user run sudo /sbin/tc qdisc del root dev eth0
without a password.
If you need to add more commands, then you can tack them onto the end with a comma like so
www-data ALL=(ALL) NOPASSWD:/sbin/tc qdisc del root dev eth0,/sbin/tc qdisc del root dev eth1
Once the sudoers file is setup, then when you run the webpage that runs the command, as long as the webpage is running sudo /sbin/tc qdisc del root dev eth0
it should work.