$\begin{align}  & ^{6}{{P}_{r}}=6 \\ & \frac{6!}{(6-r)!}=6 \\ & \text{using }r=1\text{ to test}{{\text{ }}^{6}}{{P}_{r}}=6 \\ & \frac{6!}{(6-1)!}=\frac{6!}{5!}=\frac{6\times 5!}{5!}=6 \\ & {{\therefore }^{6}}{{P}_{1}}=6 \\ & ^{6}{{P}_{r+1}}{{=}^{6}}{{P}_{1+1}}{{=}^{6}}{{P}_{2}} \\ & ^{6}{{P}_{2}}=\frac{6!}{(6-2)!}=\frac{6!}{4!}=\frac{6\times 5\times 4!}{4!}=30 \\\end{align}$