Neural computations underlying complex behavior implicate multiple brain regions and large-scale, multi-site recordings from behaving animals are becoming increasingly common. Based on simultaneous recordings across the visual cortex (V1, V2, and V4), a recent hypothesis posits that brain regions communicate through low-dimensional subspaces [Semedo et al. (2019, 2021)]. In particular, it was found that these communication subspaces are not fully aligned with the internal variability of individual areas, with some information remaining in a private subspace and the rest being communicated through a shared subspace. Most theoretical works, however, focus on modeling individual regions, with multi-area interactions only starting to be explored [e.g. Perich & Rajan (2020)]. Due to the lack of theoretical frameworks, the dynamical mechanisms governing communication through subspaces and their implications for behaviorally meaningful computations are still unclear. Here we present a mechanistic model of the communication subspace hypothesis based on low-rank recurrent neural networks [Mastrogiuseppe & Ostojic (2018)]. Concretely, we focus on a two-area network (representing A1 and PFC) that implements a context-dependent decision-making task, similar to experiments with rats [Rodgers & deWeese (2014)]. Considered in isolation, the A1 network represents incoming stimuli, while the PFC network generates a sustained representation of context. Task-solving computations emerge only when the two networks are connected through low-rank subspaces. Specifically, context information was shared through a PFC→A1 communication subspace and led to the computation of a context-dependent decision in A1 that was propagated through an orthogonal A1→PFC subspace. In contrast, stimuli information remained in a private subspace of A1, similar to what we found in single-unit recordings from rat's A1. Altogether, our model offers a mechanistic implementation of the communication subspace hypothesis, which provides a test-bed for statistical inference of multi-area interactions and derives specific predictions for analyses of multi-region recordings.