The formula for permutations is \(^{n}P_{r} = \frac{n!}{(n-r)!}\) Given that \(^{6}P_{r} = 6\), we can solve for r:

\(6 = \frac{6!}{(6-r)!}\)

\(6(6-r)! = 6!\)

\((6-r)! = \frac{6!}{6}\)

\((6-r)! = 5!\)

\((6-r) = 5\)

\(r = 1\)

Now that we know the value of r, we can find the value of \(^{6}P_{r+1}\):

\(^{6}P_{r+1} = ^{6}P_{2} = \frac{6!}{(6-2)!} = \frac{720}{24} = 30\)