6 Expand $(a+b+c+d)^{9}$ and then combine like terms, the number of terms in the resulting polynomial is ( ).
(A) $\mathrm{C}_{9}^{4}$
(D) $\mathrm{C}_{12}^{3}$
$6 \mathrm{D}$ Hint: Each term in the obtained polynomial is of the form $k a^{x_{1}} b^{x_{2}} c^{x_{3}} d^{x_{4}}$, where $k>0$,
$$
x_{1}+x_{2}+x_{3}+x_{4}=9, x_{i} \geqslant 0 .
$$

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, hence the answer is D.