Need Help with Custom ModRewrite

This can be accomplished with WordPress’s internal rewrite system by using add_rewrite_rule and adding a query var.

function wpse47506_rewrites_init(){
    add_rewrite_rule(
        'about/case-studies/([^/]+)/?$',
        'index.php?pagename=about/case-studies&clientname=$matches[1]',
        'top' );
}
add_action( 'init', 'wpse47506_rewrites_init' );

function wpse47506_query_vars( $query_vars ){
    $query_vars[] = 'clientname';
    return $query_vars;
}
add_filter( 'query_vars', 'wpse47506_query_vars' );

This would go in your functions.php file, then visit the permalinks settings page to flush rewrite rules.

You can access the value of the query var in your page template with:

<?php echo 'Hello ' . get_query_var('clientname'); ?>