Invalid HTML, might be the problem. The ENDTAG is missing an OPENTAG, so your markup is closing an element that is not open.
Aside: Since this is only an introduction, and basically a scratch on a scratch, a lot of the finer details are omitted. Your echo statement could be written with single quotes,
echo 'Greetings, ' . $name . '!';
which would be the norm. When using double quotes, it is likely more typical to see string interpolation...
echo "Greetings, $name!";
This will only work with double quotes, and as we can see is a lot more readable. PHP recognizes the variable embedded in the string.