Override Taxonomy Template

Take a look at the Codex:

• taxonomy-{taxonomy}-{term}.php – If the taxonomy were sometax, and taxonomy’s term were someterm WordPress would look for
  taxonomy-sometax-someterm.php. In the case of Post Formats, the
  taxonomy is ‘post_format’ and the terms are post-format-{format}.
  i.e. taxonomy-post_format-post-format-link.php
• taxonomy-{taxonomy}.php – If the taxonomy were sometax, WordPress would look for taxonomy-sometax.php
• taxonomy.php

You registered your taxonomy as product_categories, so you should be using taxonomy-product_categories.php to create a template for all terms in that particular taxonomy.

Use taxonomy-product_categories-furniture.php to target only the one term referenced in your URL.

taxonomy.php will be used for all taxonomies.