6. (10 points) In a cage with chickens and rabbits, there are a total of 40 heads, and the number of rabbit feet is 8 less than 10 times the number of chicken feet. Therefore, the number of rabbits is 
$$
33 \text{.}
$$
【Analysis】Let the number of rabbits be $x$, then the number of chickens is $(40-x)$. According to the multiple relationship of the number of feet: the number of rabbit feet $=$ the number of chicken feet $\times$ 10 times + 8, we can set up an equation to solve.

【Solution】Solution: Let the number of rabbits be $x$, then the number of chickens is $(40-x)$. According to the multiple relationship of the number of feet, we can set up the equation:
$$
\begin{aligned}
4 x+8 & =10 \times 2 \times(40-x) \\
4 x+8 & =800-20 x \\
x & =33
\end{aligned}
$$

Answer: There are 33 rabbits.
Therefore, the answer is: 33.