I have below machine specifications, and I have my project in Drupal 6. When I started with installation of Drupal 6 (Project), it did not give any errors with below specification.
I want to confirm before working with Drupal 6 below machine specifications that it will work properly. Otherwise I will deprecate my php version.
PHP - 5.6.26
linux - 14.4
Drupal 6
Apache/2.4.7
First, why Drupal 6 at all? It's not supported any more and Drupal 7 is really mature now and IMHO still the best choice. Drupal 8 is also progressing well and soon enough will be ready to replace Drupal 7.
Drupal 6 should run nice up to 5.4 and Drupal 6 core even on 5.6 but since you will probably using contrib modules it can be risky, so if possible my advice is to downgrade php to 5.3 to avoid eventual complications.
Here is interesting debate on that subject:
https://www.drupal.org/node/2465881
But if you decide to go with php 5.6 after all check out this article:
http://www.mediacurrent.com/blog/getting-your-drupal-6-site-ready-run-php-56