Second Binomial Value

If $\left(\genfrac{}{}{0ex}{}{n}{12}\right)=\left(\genfrac{}{}{0ex}{}{n}{8}\right)$, find $\left(\genfrac{}{}{0ex}{}{22}{n}\right)$.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XI. Permutations and Combinations, Examples XI.a, No. 16 (part 2)