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