2) $$\left(\frac{a+4}{a-4} - \frac{a-4}{a+4}\right) : \frac{48a}{16-a^2}$$.

$$\left(\frac{a+4}{a-4} - \frac{a-4}{a+4}\right) : \frac{48a}{16-a^2} = \left(\frac{(a+4)^2 - (a-4)^2}{(a-4)(a+4)}\right) : \frac{48a}{16-a^2} = \left(\frac{(a^2+8a+16) - (a^2-8a+16)}{a^2-16}\right) : \frac{48a}{16-a^2} = \frac{a^2+8a+16-a^2+8a-16}{a^2-16} : \frac{48a}{16-a^2} = \frac{16a}{a^2-16} : \frac{48a}{16-a^2} = \frac{16a}{a^2-16} \cdot \frac{16-a^2}{48a} = \frac{16a}{a^2-16} \cdot \frac{-(a^2-16)}{48a} = \frac{16a \cdot -(a^2-16)}{48a (a^2-16)} = -\frac{1}{3}$$