Display Custom Taxonomy names

it looks like your get_terms() call is incorrect, the argument is not an array and you have a typo in taxonomy name (‘product_category’ instead of ‘product_categories’) it should be

<?php 
$terms = get_terms( array( 
    'taxonomy'=>'product_categories', 
    'hide_empty'=> false 
) ); 
?>

If this will not help it would be best if you could let us know if you are seeing any error message and if you do paste the error here.