Answer
$_4P_4=24$
Work Step by Step
RECALL:
$_nP_r = \dfrac{n!}{(n-r)!}$
Use this definition to have:
$\require{cancel}
_4P_4=\dfrac{4!}{(4-4)!}
\\_4P_4=\dfrac{4!}{0!}
\\_4P_4 = \dfrac{4!}{1}
\\_4P_4 = 4!
\\_4P_4=4(3)(2)(1)
\\_4P_4=24$