Search form with Category and Sub Category

First you have to give your dropdown names so:

<?php $media = array(
 'name'               => 'subcat',
 'hierarchical'       => 1,
 'parent'             => get_cat_id('Media'),
 'show_option_none'   => ('All Media'),
 'hide_empty'   => 0  ); 
?>

<form method="get" id="searchform" action="<?php bloginfo('url'); ?>/">
  <div>
    <input type="text" value="<?php the_search_query(); ?>" name="s" id="s" />
    <?php wp_dropdown_categories('name=maincat&show_option_none=All Category'); ?>
    <?php wp_dropdown_categories($media); ?>
    <input type="hidden" id="my_search" name="my_search" value="c_search" />
    <input type="submit" id="searchsubmit" value="search" />
  </div>
</form>

Then create you search filter

// Define search filter
function search_filter( $query ) {
    // only modify your custom search query.
    if ( $query->is_search &&  $_post['my_search'] == "c_search") {
        $args = array(
                'relation' => 'AND',
            array(
                'taxonomy' => 'category',
                'field' => 'id',
                'terms' => array( $_post['maincat']),
                'operator' => 'IN'
            ),
            array(
                'taxonomy' => 'category',
                'field' => 'id',
                'terms' => array( $_post['subcat']),
                'operator' => 'IN'
            )
        );
        $query->set( 'tax_query', $args);
    }
    return $query;
}

// The hook needed to search_filter
add_filter( 'the_search_query','search_filter');