For example, in the sequence $x_{1}, x_{2}, \cdots, x_{n}, \cdots$, the sum of any three consecutive terms is 20, and $x_{1}=9, x_{12}=7$. Find the value of $x_{2000}$.
Given that $x_{n+1}+x_{n+2}+x_{n+3}=20$
$$
x_{n}+x_{n+1}+x_{n+2}=20
$$

Subtracting the two equations, we get $x_{n+3}=x_{n}(n \geqslant 1)$. Therefore, $\left\{x_{n}\right\}$ is a periodic sequence with a period of 3, so $x_{4}=x_{1}=9, x_{12}=$ $x_{3}=7$. Since $x_{1}+x_{2}+x_{3}=20$, we have $x_{2}=4$. Hence, $x_{2000}=x_{2}=4$