Calculate: (8!*4!)/(7!*6!)

Expression: $\frac{8!\cdot 4!}{7!\cdot 6!}$

Cancel the factorials $\frac{n!}{\left(n-m\right)!}=n\cdot \left(n-1\right)\cdots \left(n-m+1\right),\quad n\gt m$

$=\frac{8\cdot 4!}{6!}$

Cancel the factorials $\frac{n!}{\left(n+m\right)!}=\frac{1}{\left(n+1\right)\cdot \left(n+2\right)\cdots \left(n+m\right)}$

$=\frac{8}{5\cdot 6}$

Cancel $\frac{8}{5\cdot 6}:{\quad}\frac{4}{5\cdot 3}$

$=\frac{4}{5\cdot 3}$

Multiply the numbers: $ 5\cdot 3=15$

$=\frac{4}{15}$