$$
\begin{array}{l}
\text { 6. Let }(1+2 \sqrt{2}+3 \sqrt{3})^{n} \\
=a_{n}+b_{n} \sqrt{2}+c_{n} \sqrt{3}+d_{n} \sqrt{6} \text {, }
\end{array}
$$

where, $a_{n}, b_{n}, c_{n}, d_{n} \in \mathbf{N}$.
Then $\lim _{n \rightarrow+\infty} \frac{d_{n}}{a_{n}}=$ $\qquad$