\[\frac{x^{2} - 4}{x - 2} = 4,\ \ x \neq 2\]
\[x^{2} - 4 = 4 \cdot (x - 2)\]
\[x^{2} - 4 = 4x - 8\]
\[x^{2} - 4x - 4 + 8 = 0\]
\[x^{2} - 4x + 4 = 0\]
\[(x - 2)^{2} = 0\]
\[x - 2 = 0\]
\[x = 2 - не\ подходит.\]
\[Ответ:нет\ решения.\]