6. After expanding and combining like terms of $(a+b+c+d)^{9}$, the number of terms in the resulting polynomial is ( ).
(A) $\mathrm{C}_{9}^{4}$
(B) $\mathrm{C}_{9}^{3}$
(C) $\mathrm{C}_{12}^{4}$
(D) $\mathrm{C}_{12}^{3}$
6. D.
Each term in the obtained polynomial is of the form
$$
k a^{x_{1}} b^{x_{2}} c^{x_{3}} d^{x_{4}}(k>0) \text {. }
$$

Thus, $x_{1}+x_{2}+x_{3}+x_{4}=9\left(x_{i} \geqslant 0\right)$.
It is easy to see that the above equation has $\mathrm{C}_{9+4-1}^{4-1}=\mathrm{C}_{12}^{3}$ sets of integer solutions.