Relation Between Indices

Find the relation between $r$ and $n$ in order that the coefficients of the $3r^{\text{th}}$ and $(r+2{)}^{\text{th}}$ terms of $(1+x{)}^{2n}$ may be equal.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIII. Binomial Theorem: Positive Integral Index, Examples XIII.b, No. 15