We prove that counting 2-factors (i.e., spanning 2-regular subgraphs or vertex disjoint cycle covers) of 4-regular bipartite graphs is \(\#P\) -complete under many-one counting (“weakly parsimonious”) reductions. This resolves a missing case in a proof by (Felsner & Zickfeld; Electron. J. Combin. 15(1), R77; 2008) that counting 2-factors of k-regular bipartite graphs is \(\#P\) -complete \(\forall \left( k \ge 3 \ | \ k \ne 4\right) \) and, due to a bijective correspondence, establishes the same hardness result for counting the Eulerian orientations of 4-regular bipartite graphs.