[php] How can I run a PHP script inside a HTML file?

You can't run PHP in an html page ending with .html. Unless the page is actually PHP and the extension was changed with .htaccess from .php to .html

What you mean is:

index.html
<html>
...
<?php echo "Hello world";?> //This is impossible


index.php //The file extension can be changed using htaccess, ex: its type stays php but will be visible to visitors as index.html

<?php echo "Hello world";?>