To have full control over what is displayed on each page, you’d do best to create a Child Theme. Basically, you create a style.css file with specific comments at the top, so WordPress recognizes your files as a theme. Then, you copy any of WooCommerce’s files where you need customization, and place them into your child theme. You can then edit the PHP in just those files to remove things like the brand.
As to your code snippet, any PHP must be wrapped inside <?php ... ?> tags or the server won’t recognize it as PHP. So add <?php and ?> around add_filter, like so:
<?php add_filter( 'pwb-single-product-brands', _'return_false'); ?>
<!DOCTYPE html>
<!--[if IE 8]>
<html xmlns="http://www.w3.org/1999/xhtml" class="ie8 wp-toolbar" lang="en-US">
<![endif]-->
<!--[if !(IE 8) ]><!-->
<html xmlns="http://www.w3.org/1999/xhtml" class="wp-toolbar" lang="en-US">
<!--<![endif]-->
<head>
But, normally you don’t use add_filter inside the same file where your DOCTYPE and basic HTML start – those are usually in your theme’s header.php file, and filters belong ideally in a plugin, or second-best in a child theme’s functions.php file.