This paper studies the shuffling phase in a distributed computing model with rate-limited links between nodes. Each node is connected to all other nodes via a noiseless broadcast link with a finite capacity. For this network, the shuffling phase is described as a distributed index-coding problem to extend an outer bound for the latter to the distributed computing problem. An inner bound on the capacity region is also established by using the distributed composite-coding scheme introduced for the distributed index-coding problem. We consider some special cases of the distributed computing problem through two examples for which we prove that the inner and outer bounds agree, thereby establishing the capacity regions. We, then, generalize the special cases to any number of nodes and computation loads under certain constraints.