The "get_the_ID()" function is used incorrectly, and can be left out. Your code becomes:
$children = get_children( array( 'post_parent' => 4 ) );
You might also want to specify the post_type parameter. Now your function will also return attachments.
$children = get_children( array( 'post_parent' => 4, 'post_type' => 'page' ) );