How do zen practitioners balance the mix between Buddhism detachment and Taoism attachment? On this site there's a topic Is there common ground between the Tao Te Ching and Buddhism? where one of the answers says:


  A commentator of the Taoist philosopher Guo Xiang's work and a Taoist himself, I forget his name now (I can look it up) once wrote that - I paraphrase from memory - Buddhism and Taoism are diametrically opposed, because one seeks detachment from all existence, while the other seeks attachment to all existence. One seeks liberation by detaching from all phenomena, while the other seeks liberation by becoming one with all phenomena. The two paths seem to be the same, but really they are opposite.


And in an answer to the topic Are there many differences between Taoism and Buddhism?:


  Buddhism seeks to transcend suffering while Taoism seeks unity with nature


So they don't necessary mutually exclusive each other, and of course one can combine it in zen.

But how do practitioners do that exactly?

How do they seek detachment and attachment at the same time?



FYI: Detachment (philosophy)
To say that Zen = Buddhism + Taoism is an utter simplification. To say that Buddhism seeks "detachment from all existence" is not at all accurate and to say that Taoism seeks "attachment to all existence" is a caricature.

And yet I will answer this question on its own terms, to help you clear your doubts:

If you detach from all existence, completely 100%, at the end there won't be "you". If you unite with all existence, completely 100%, at the end there won't be "you". In both cases the result is the same.

That said, you should study the Goal of Buddhism (Nirvana or Enlightenment) and the Goal of Taoism (living in harmony with the Tao) to understand what both of them really mean, so you can go beyond simplistic definitions and understand what this is actually about.