How to Manually Code Shortcode?

Your code is badly broken.

1. You start a function definition but never finish it. There is no
   associated } to end the function.
2. You start an if conditional and never close it.
3. You start a while loop and never close it.

Those are why your page won’t load with that code. You are getting a fatal PHP error and would be getting multiple fatal errors if the whole script didn’t bail at the first one. If you have debugging enabled you would see that.

1. You are also using output buffering in a way that doesn’t do
   anything at all, and if I am not mistaken in a way that will cause the rest of the page to fail to display even if you didn’t have the fatal errors.

Additionally, your Loop wouldn’t output anything anyway as you haven’t included any code that actually echos post information. The minimal fixes you need are:

And you are passing category information into the shortcode but have a category hard-coded into the query. I’ve altered your defaults to compensate.

function vntd_blog_carousel($atts, $content = null) {
  extract(shortcode_atts(array(
      "cats" => 6, // default cat, if any
      "posts_nr" => '',
      "thumb_style" => ''
  ), $atts));

  wp_enqueue_script('prettyPhoto', '', '', '', true);
  wp_enqueue_style('prettyPhoto');

  wp_enqueue_script('owl-carousel', '', '', '', true);
  wp_enqueue_style('owl-carousel');

  ob_start();

  echo '<div class="vntd-portfolio-carousel blog-carousel"><div class="works white">';

  $size="portfolio-square";

  $args = array(
      'posts_per_page' => 6,
      'cat'       => $cats,
      'orderby'   => 'slug'
  );
  $the_query = new WP_Query($args); 

  if ($the_query->have_posts()) {
    while ($the_query->have_posts()) {
      $the_query->the_post();
      // echo some post data
      the_title();
      the_content();
    } // close the while Loop
  } // close the if conditional

  wp_reset_postdata(); // moved from before the Loop where it really wasn't doing any good

  return ob_get_clean(); // use the output buffer that you've created
} // close the function definition.

See the code comments for exactly what I did. I have also formatted the code for readability and removed that nightmarish alternative control syntax, which is only good for crazy-making.

To turn the whole thing into a shortcode all you need is:

add_shortcode('vntd_blog_carousel','vntd_blog_carousel');

And to manually run it use:

do_shortcode('[vntd_blog_carousel cats="2"]');

I have no idea what the other two shortcode attributes are supposed to do.