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<h1>Solución</h1>
<p>
Para clasificar la discontinuidad en el punto $2$ debemos evaluar $\mathop {\lim }\limits_{x \to 2} f\left( x \right)$:
$$\begin{aligned}
   \mathop {\lim }\limits_{x \to 2} f\left( x \right) &= \mathop {\lim }\limits_{x \to 2} {{{x^2} - 4} \over {x - 2}}  \\
  &  = \mathop {\lim }\limits_{x \to 2} {{\left( {x + 2} \right)\left( {x - 2} \right)} \over {x - 2}}  \\
  &  = \mathop {\lim }\limits_{x \to 2} \left( {x + 2} \right)  \\
  &  = 4
  \end{aligned}$$
Dado que $f$ es discontinua en $2$ y $\mathop {\lim }\limits_{x \to 2} f\left( x \right)$:
existe, $f$ tiene una discontinuidad removible o evitable en $x = 2$.

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