The square brackets in your code are used in the mysql documentation to indicate groups of optional parameters. They should not be in the actual query.
The only command you actually need is:
show tables;
If you want tables from a specific database, let's say the database "books", then it would be
show tables from books;
You only need the LIKE part if you want to find tables whose names match a certain pattern. e.g.,
show tables from books like '%book%';
would show you the names of tables that have "book" somewhere in the name.
Furthermore, just running the "show tables" query will not produce any output that you can see. SQL answers the query and then passes it to PHP, but you need to tell PHP to echo it to the page.
Since it sounds like you're very new to SQL, I'd recommend running the mysql client from the command line (or using phpmyadmin, if it's installed on your system). That way you can see the results of various queries without having to go through PHP's functions for sending queries and receiving results.
If you have to use PHP, here's a very simple demonstration. Try this code after connecting to your database:
$result = mysql_query("show tables"); // run the query and assign the result to $result
while($table = mysql_fetch_array($result)) { // go through each row that was returned in $result
echo($table[0] . "<BR>"); // print the table that was returned on that row.
}