\[\frac{24p^{6}}{35q^{4}} \cdot \frac{49q}{16p^{4}} = \frac{24p^{6} \cdot 49q}{35q^{4} \cdot 16p^{4}} =\]
\[= \frac{6 \cdot 7p^{2}}{5 \cdot 4q^{3}} = \frac{21p^{2}}{10q^{3}}\]