Remove “Content” and “Discussion” from Right Now Dashboard Widget

Here are two methods:

Method 1

You could remove the whole Right Now metabox from your dashboard:

function custom_dashboard() {
    if(!current_user_can('manage_options')){
    // only remove it for non-admins
        remove_meta_box('dashboard_right_now', 'dashboard', 'core');
    }
}
add_action('admin_init','custom_dashboard');

and then add another custom Right Now metabox with your custom code. You could for example check out the WordPress function wp_dashboard_right_now() located in /wp-admin/includes/dashboard.php.

Method 2

You could hide the .table_content and .table_discussion parts via CSS:

function custom_css() {
    if(!current_user_can('manage_options')){
        // only hide it for non-admins
        echo "<style>#dashboard_right_now .table_content, #dashboard_right_now .table_discussion {display:none !important;}</style>";
    }
}
add_action('admin_head-index.php','custom_css');

and the metabox will look similar to this one in your dashboard: