Answer
$70$
Work Step by Step
Cancelling the common factors between the numerator and the denominator, the given expression, $
\dfrac{8\cdot7\cdot5\cdot6}{4\cdot3\cdot2\cdot1}
,$ is equivalent to
\begin{align*}\require{cancel}
&
\dfrac{\cancel8\cdot7\cdot5\cdot6}{\cancel4\cdot3\cdot\cancel2\cdot1}
\\\\&=
\dfrac{7\cdot5\cdot6}{3\cdot1}
\\\\&=
\dfrac{7\cdot5\cdot\cancel6^2}{\cancel3\cdot1}
\\\\&=
7(5)(2)
\\&=
70
.\end{align*}
Hence, the given expression simplifies to $
70
.$
