Completing the solution of the directed Oberwolfach problem with two tables

We address the last outstanding case of the directed Oberwolfach problem with two tables of different lengths. Specifically, we show that the complete symmetric directed graph $K_n^{\ast }$ admits a decomposition into spanning subdigraphs comprised of two vertex-disjoint directed cycles of length $t_1$ and $t_2$, respectively, where $t_1\in \{4,6\}$, $t_2$ is even, and $t_1+t_2⩾14$. In conjunction with recent results of Kadri and Šajna, this gives a complete solution to the directed Oberwolfach problem with two tables of different lengths.