Filter two vocabularies in Drupal 7
This is not a standardfeature of Taxonomy. In fact, it is not a part of the concept Taxonomy, regardless of using Drupal at all. 

However, you can achieve this, somehow with Drupal taxonomies, when you abuse them as Facets. 

For that, you need to set up your views and provide quite some hacks, amongst others, you need to add some PHP to your views. 

From a birdseye, here is what you do:


You create views that list only nodes with term X as parameter: /mypage/12 to show only pages with term 12.
You allow Drilling down in that list, by nesting the parameters: /mypage/12/35 to show only nodes with BOTH term 12 AND term 35.
You abuse the views header to present links with options: links to the nested options: on mypage/12 it would show, amongst others, a link to term 35, a link to /mypage/12/35.
The code to select these options can be simplified by making a second view: a view that lists all options nested under 12. 
In the header of the first, node, view, you then place some PHP that fetches and renders these links. 


For a long and detailed howto, I think burningbird has a good manual