https://hostname.example.com:2087/cpsess###########/json-api/cpanel?cpanel_jsonapi_user=user&cpanel_jsonapi_apiversion=2&cpanel_jsonapi_module=MysqlFE&cpanel_jsonapi_func=getdbuserprivileges&dbuser=username&db=example_database

$cpanel = new CPANEL(); // Connect to cPanel - only do this once.
 
//  Retrieve the permissions that a database user has on a database
$get_permissions = $cpanel->api2(
    'MysqlFE', 'getdbuserprivileges',
        array(       
            'dbuser'      => 'username',
            'db'          => 'example_database',
    )
);

my $cpliveapi = Cpanel::LiveAPI->new(); # Connect to cPanel - only do this once.
 
# Retrieve the permissions that a database user has on a database
my $get_permissions = $cpliveapi->api2(
    'MysqlFE', 'getdbuserprivileges',
    (       
            'dbuser'      => 'username',
            'db'          => 'example_database',
    )
);

cpapi2 --user=username MysqlFE getdbuserprivileges dbuser=username db=example_database

 {
  "cpanelresult": {
    "apiversion": 2,
    "data": [
      "ALTER",
      "CREATE ROUTINE",
      "CREATE TEMPORARY TABLES",
      "DROP",
      "INSERT",
      "LOCK TABLES",
      "SHOW VIEW",
      "TRIGGER"
    ],
    "func": "getdbuserprivileges",
    "event": {
      "result": 1
    },
    "module": "MysqlFE"
  }
}