There are more ways to show list a MySQL databases in PHP. PDO (PHP Data Objects) is the best of them.
Advantages of PDO is a consistent interface across many different types of database, uses an object-oriented approach, and supports more features offered by newer databases.

Using a PDO recommends wherever possible.

How to show lists databases on MySql server - Example


$user "your_username";
$password "your_password";
$dbh = new PDO"mysql:host=$host"$user$password );
$dbs $dbh->query"SHOW DATABASES" );

while( ( 
$db $dbs->fetchColumn) ) !== false )