How to display meta_value array?

The SQL you want would be:

$sql = "
  SELECT DISTINCT post_id 
  FROM $wpdb->posts, $wpdb->postmeta 
  where $wpdb->postmeta.meta_value="2015/06/03"";
$results =$wpdb->get_results($sql);

But there is no reason to be involving the $wpdb->posts table at all, since the post_id value is a $wpdb->postmeta table column.

$sql = "
  SELECT DISTINCT post_id 
  $wpdb->postmeta 
  where $wpdb->postmeta.meta_value="2015/06/03"";
$results =$wpdb->get_col($sql);

Note that I changed $wpdb->get_results to wpdb->get_col as you are only returning a single column of data. The results will come out needing less manipulation afterward.

You could also skip the DISTINCT and use PHP’s array_unique():

$sql = "
  SELECT post_id 
  $wpdb->postmeta 
  where $wpdb->postmeta.meta_value="2015/06/03"";
$results =$wpdb->get_col($sql);
$results = array_unique($results);

However, the far more correct way would be to use WP_Query. I was going to suggest that but then noticed that you are not searching for a meta_key at all, but are searching the whole table. That is going to cause trouble eventually. Suppose some plugin stores data in the $wpdb->postmeta table with that date format? Then your code will retrieve those values as well, which is certainly not intended behavior. Someone could even enter such dates as a custom field right from the stock post edit panel. You should specify a key, something like:

$args = array(
  'fields' = 'ids',
  'ignore_sticky_posts' => true,
  'meta_query' => array(
    array( 
      'key' => 'my_date_key',
      'value' => '2015/06/03',
    )
  )
);
$pids = new WP_Query($args);

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