Wakuan said, "Why has the Western Barbarian no beard?"
Study should be real study, enlightenment should be real enlightenment. You should once meet this barbarian directly to be really intimate with him. But saying you are really intimate with him already divides you into two.
Don't discuss your dream
Before a fool.
Barbarian with no beard
Obscures the clarity.
Most koans will bring the concept of non-duality wrapped in easier to digest--though still no by no means "easy"--side issues. "Mu" discards the duality of "correct" and "incorrect," but does so by challenging the student to give up set ideas in total. Hyakujo's Fox also deals with correctness, but more so dissolves the separation of self from the flow of cause and effect, but does so with a parable that gives the reader a narrative to follow. The Western Barbarian's Beard, on the other hand, is not gentle in testing you. It's a sudden shove out of the nest. You will fly or you will plummet.
The Western Barbarian is a description associated with Bodhidharma, the Indian monk who, according to tradition, brought Zen to China. He is always depicted as having a full, bushy beard. Wakuan asks "Why is it that he doesn't have a beard?" This is similar to Joshu's "Mu." It is a question that already assumes what we understand to be an incorrect fact. Wakuan is looking you in the eye and saying: "Do you believe you are a person of Zen? Here's your test: Bodhidharma has a beard; why doesn't he have a beard? Have fun plummeting!"
It is in Mumon's comment that you get your only hint, your only nudge toward understanding. He suggests that, in discovering enlightenment, you should find yourself "intimate" with this barbarian--but that saying that you are intimate with him already divides you in two. This is one of the most direct statements in Zen, but its brevity, and the connection with the concept of being "intimate" with a long-dead figure infuse it with a sense of mysticism that your mind will use to obscure the simple, concise instruction.
Mumon is telling you that you need to discard the concept of duality. Of the self versus other. Of subject-and-object. You do not become intimate with the barbarian, you recognize that you and the barbarian are not separate, and that separation is a delusion. That the barbarian and his beard are also not two separate things. He cannot "have" his beard, because identifying "him" and "his beard" is an act that cuts out two pieces of the universe which are not independent of each other, or you, or of anything else.
This is not something you can think your way out of. Even if you recognize the concept of this duality, and recognize the principle of discarding it, you are not free from it. But when your thinking is exhausted, and your understanding is stretched thin, if something is able to punch through your conceptual thinking--be it Joshu's Mu, Goso's Buffalo, or even something from your own mundane life--then all of the division is cast aside, and Bodhidharma has no beard. Until then, Wakuan's shove is a merciless reminder of the delusion of understanding.