"public_html" is your web root. It is represented in URL or href paths (but not filesystem paths!) by "/". So the path to your template file needs to be relative to where the index.php file is, and the index.php file is most likely in your web root. The path then would simply be "assets/snippets...". No leading / and no leading public_html.
[[Template? &template_file=`assets/templates/mytemplate/template.html`]]
You can name the file anything you like, also the folder you put it in. You just need to point that path at whatever it is.
The full path would look something like this (remember, it’s a file you are including, so the URL type path won’t work):
/servername/users/myusername/public_html/assets/templates/mytemplate/template.html
Note the leading / that indicates that the path starts at the root of the filesystem on the server.