Tomamos como el límite
$$\lim_{x \to 2^+}\left(\frac{- 4 x + \left(x^{2} + 4\right)}{- 10 x + \left(x^{2} + 6\right)}\right)$$
cambiamos
$$\lim_{x \to 2^+}\left(\frac{- 4 x + \left(x^{2} + 4\right)}{- 10 x + \left(x^{2} + 6\right)}\right)$$
=
$$\lim_{x \to 2^+}\left(\frac{\left(x - 2\right)^{2}}{x^{2} - 10 x + 6}\right)$$
=
$$\lim_{x \to 2^+}\left(\frac{\left(x - 2\right)^{2}}{x^{2} - 10 x + 6}\right) = $$
$$\frac{\left(-2 + 2\right)^{2}}{- 20 + 2^{2} + 6} = $$
= 0
Entonces la respuesta definitiva es:
$$\lim_{x \to 2^+}\left(\frac{- 4 x + \left(x^{2} + 4\right)}{- 10 x + \left(x^{2} + 6\right)}\right) = 0$$