there are different content types and associated with different taxonomies. for example forum content type associated forum taxonomy, article content type is associated with tag taxonomy and gallery content type is associated with gallery taxonomy. i want to show related contents in front page blog, but taxonomies different. how can i associate them? with using only one taxonomy for all content types or else?
Forum and Gallery taxonomies are used to maintain the information structure of their respective content types. They should not be mixed.
A tagging taxonomy, on the other hand, is generally freestyle, and allows a user to give keywords describing the content. There is no reason to restrict it to a single content type. Why not use your tags on all content types.
Taxonomy fields, like any field, may be attached to multiple content types. It sounds like the view you're displaying on your home page needs to draw from one taxonomy. Therefore, your options are to use one taxonomy across all of the content types, or to build a different view with a better way to implement your concept of "related content."