6. Let $a, b, c$ be distinct rational numbers, satisfying $(b+\sqrt{2})^{2}=(a+\sqrt{2})(c+\sqrt{2})$.
Then the number of sets of $a, b, c$ that satisfy the condition is ( ).
(A) 0
(B) 1
(C) 2
(D) 4
6. A.

Since $(b+\sqrt{2})^{2}=(a+\sqrt{2})(c+\sqrt{2})$, that is, $b^{2}+2+2 \sqrt{2} b=a c+2+(a+c) \sqrt{2}$, then $a c=b^{2}, a+c=2 b$.
Thus, $a^{2}+c^{2}+2 a c=(a+c)^{2}=4 b^{2}=4 a c$.
Therefore, $(a-c)^{2}=0$.
Hence, $a=c$, which contradicts the given condition.