Answer
r=3
There is not enough information for n
Work Step by Step
${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!},\quad {}_{n}C_{r}=\frac{n!}{(n-r)!r!}$
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We see that ${}_{n}P_{r}=r!\cdot {}_{n}C_{r}$
The text gives: ${}_{n}P_{r}=6\cdot {}_{n}C_{r}$, so
$r!=6=3!$
$r=3$
${}_{n}P_{3}=3!\cdot {}_{n}C_{3}$ is true for ANY $n \geq 3 $,
So, we need more information to determine n.