Let us say we've the next menu structure:

menu #1
menu #2
menu #3
- submenu #1
-- subsubmenu #1
-- subsubmenu #2
-- subsubmenu #3
- submenu #2
- submenu #3
menu #4
menu #5

In WordPress how do i show on the landing/home page (index.php hard coded) this content from the #subsubmenu #2 and #subsubmenu #3 which suppose would be the latter added subsubpages underneath the #submenu #1 page?

I adopted the suggestions through the next page:

http://codex.wordpress.org/Function_Reference/query_posts

I made use of the following code:

<?php query_posts('post_parent=12&posts_per_page=2'); ?>
                <?php if ( have_posts() ) : while ( have_posts() ) : the_post(); ?>
                <h3><a href="<?php the_permalink() ?>" rel="bookmark"><?php the_title(); ?></a></h3>
                <div class="entry">
                    <p><?php the_excerpt(); ?></p>
                </div>
                <?php endwhile; else : ?>
                <?php endif; ?>
                <?php wp_reset_query(); ?>

No success. Any suggestions?

You should use an order by menu_order parameter for the query, and getting a climbing down to get it sorted out.

Note: you have to make use of the menu_order attribute underneath the Page Attribute Box, in the right from the edit screen

Rewrite your quey as

See: http://codex.wordpress.org/Function_Reference/query_posts#Order_.26_Orderby_Parameters

I attempted also: <?php query_posts('post_parent=6/12&posts_per_page=2&menu_order&order=DESC'); ?>. And can show some posts which i don't have to be proven. I believed which will appear the final two added child pages of parent page with id 6 and subpage with id 12. Still no success :(