XPath makes it simple, assuming that's the only text input with "make" as its name:
$dom = new DOMDocument();
$dom->loadHTML(...);
$xp = new DOMXpath($dom);
$nodes = $xp->query('//input[@name="make"]');
$node = $nodes->item(0);
$car_make = $node->getAttribute('value');
If there's more than one input with that particular field name on the page (which is entirely possible), then you'll have to do some extra work to narrow down WHICH of those multiple inputs you want.
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