Answer
$19,958,400$
Work Step by Step
Using $P(n,r)=\dfrac{n!}{(n-r)!},$ the given expression, $P(
12,8
),$ evaluates to
\begin{array}{l}\require{cancel}
=\dfrac{12!}{(12-8)!}
\\\\=
\dfrac{12!}{4!}
\\\\=
\dfrac{12(11)(10)(9)(8)(7)(6)(5)(\cancel{4!})}{\cancel{4!}}
\\\\=
19,958,400
\end{array}