12.1 $\lim _{x \rightarrow 2} \frac{x^{3}-8}{2 x-4}$.
12.1 The function $f(x)=\frac{x^{3}-8}{2 x-4}$ is undefined at the point $x=2$. By factoring the numerator using formula (1.14), we can represent this function as

$f(x)=\frac{(x-2)\left(x^{2}+2 x+4\right)}{2(x-2)}$.

In the domain of the function $f(x)$, the expression $x-2 \neq 0$, so the fraction can be simplified by canceling out $x-2$. Then we get

$$
\lim _{x \rightarrow 2} f(x)=\lim _{x \rightarrow 2} \frac{x^{2}+2 x+4}{2}=f(2)=6
$$

Answer: 6.