This paper addresses the problem of finding fair directions in a task graph, where each vertex represents an agent and each edge represents a task. A task has a marginal utility of 0 for an agent if the corresponding edge is not adjacent to the agent. Zhou et al. (IJCAI, 2024) analyzed the complexity of determining the EFX direction in a mixed graph of goods and tasks and conjectured that determining the EFX direction in a graph containing only tasks is NP-complete. This paper addresses this conjecture by providing a polynomial-time algorithm for finding the EF1 and EFX directions in a graph containing only tasks (even in the presence of self-loops). Remarkably, this result shows a striking difference between the cases of goods and tasks. Furthermore, this paper demonstrates the NP-completeness of the EF1 and EFX direction problems for multigraphs.