To understand how to use Theme Hook Suggestions, please refer to the documentation at: Drupal 7 Template (Theme Hook) Suggestions
base template: node.tpl.php
Theme hook suggestions are made based on these factors, listed from
the most specific template to the least. Drupal will use the most
specific template it finds:
base template: page.tpl.php
The suggestions are numerous. The one that takes precedence is for the
front page. The rest are based on the internal path of the current
page. Do not confuse the internal path to path aliases which are not
accounted for. Keep in mind that the commonly-used Pathauto module
uses path aliases.
The front page can be set at "Administration > Configuration > System
Site information." In Drupal 6, at "Administrator > Site configuration > Site information." Anything set there will trigger the
suggestion of "page--front.tpl.php" for it.
The list of suggested template files is in order of specificity based
on internal paths. One suggestion is made for every element of the
current path, though numeric elements are not carried to subsequent
suggestions. For example, "http://www.example.com/node/1/edit" would
result in the following suggestions:
It can be done in a variety of ways (at the page level as well). You can also provide your own suggestions in a preprocess function.
In your case you have not defined a new content type, but have used the Basic Page type, and you want to do it for a single page only. You therefore need to get the node id of your page, and then override as follows:
In your case, as you indicated that you wish to override the page.tpl.php file, it will be the latter.