the action of the form is set to post to the quote-thankyou.php page.
when working with forms, always keep the following rule in mind:
All Form Processing MUST occur on the page specified as the action.
in this case, you need to apply the server validation behavior to validate the captcha input on the quote-thankyou.php page.
see this page for more details on adding server validation:
as for the captcha image not showing up on the server, when i right click the captcha placeholder and selct open in a new tab, it brings me to a page not found error:
this indicates that the files from the webassist/captcha/ folder have not been uploaded to the server.