Few things.
Don't use short tags: <?= ... ?> use <?php echo ...; ?> instead.
Although it works, using double quotes about attribute values and using lowercase tag selectors should ensure your html can validate in a number of !doctypes: <SELECT name=make> could be <select name="make">
BTW, there's no !doctype - so this may trigger quirksmode in some browsers:
So use, e.g.
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
for xhtml transitional or
<!DOCTYPE html>
for html5
It's usually a good move to separate form handling code from the form logic into separate files. THis ensures that page refreshes do not send the form data twice. Often this is not a problem, but it could be if you're posting data to a DB.
Anyway, in order to get the selected item to show in the dropdown, you can check the $_POST variable and modify the 'build options code':
BUT your bigegst problem here is that you're calling a php function from a js call (onchange). You can't do this - only via Ajax. JS deals with data on the client (browser) - it can't access php code (on the server) unless it goes via XMLHttpRequest (or the ActiveX object equivalent for early versions of IE).
This sounds really complicated, but using a library like jQuery can make it a breeze.
Come back if you don't understand what I'm getting at.