6. A die is a cube, with the six faces engraved with $1$, $2$, $3$, $4$, $5$, $6$. There are 10 uniform dice. Throwing 4 dice and 3 dice at once, the ratio of the probabilities of getting the sum of the points on the faces of each die as 6 is
6. 6: 1 .

The situation of rolling a 6 with three dice is
$$
1,1,4 ; 1,2,3 ; 2,2,2 \text {. }
$$

There are a total of $3+3!+1=10$ ways, with a probability of $\frac{10}{6^{3}}$.
The situation of rolling a 6 with four dice is $1,1,1,3 ; 1,1,2,2$.
There are a total of $4+\mathrm{C}_{4}^{2}=10$ ways, with a probability of $\frac{10}{6^{4}}$. Therefore, the ratio of the probabilities is $\frac{10}{6^{3}}: \frac{10}{6^{4}}=6: 1$.