6. (B).

Let the real part of the expansion be $f(x)$, and the imaginary part be $g(x)$, then $f(1)$ and $g(1)$ are the sums of the coefficients of the real part polynomial and the imaginary part polynomial, respectively.
$$\begin{array}{l} f(1)+i g(1)=(1+i)^{4 n+2} \\ =2^{2 n+1}\left(\cos \frac{\pi}{4}+i \sin \frac{\pi}{4}\right)^{i n+2} \\ =2^{2 n+1}\left[\cos \left(n \pi+\frac{\pi}{2}\right)+i \sin \left(n \pi+\frac{\pi}{2}\right)\right] . \\ =2^{2 n+1} \cdot(-1)^{n} i \end{array}$$

It is a pure imaginary number, so $f(1)=0$.