\[\frac{7x + 7y}{a^{4}} \cdot \frac{6a^{8}}{x^{2} - y^{2}} =\]
\[= \frac{7 \cdot (x + y) \cdot 6a^{8}}{a^{4} \cdot (x - y)(x + y)} = \frac{42a^{4}}{x - y}.\]