view content by two taxonomy terms from two vocabulary
In Views you can do it with Exposed filters.

Just add filtering by your two vocabularies to your view (FILTER CRITERIA) an set each filter "Expose this filter to visitors, to allow them to change it". That will show form to enter taxonomy tags to filter on views page. AND logic "show the contents tagged with both terms" works by default (set each exposed filter to "required" if you dont want to allow "all", that way user must select something).