This paper presents a theoretical framework for the synthesis of tetrahex-carbon, a predicted two-dimensional carbon allotrope made up of alternating four-membered and six-membered rings. It argues that current biphenylene-based approaches run into a topological limitation and proposes a more rational precursor-design strategy for guiding on-surface synthesis toward the tetrahex lattice. The proposed route uses functionalized benzocyclobutadiene-derived precursors that can couple through four-membered-ring reactive sites on metal surfaces under ultra-high-vacuum conditions. The framework also gives testable predictions for lattice structure, electronic behavior, and STM/STS signatures that could be checked experimentally.the goal of this work is to provide a starting point for future computational and experimental studies on tetrahex-carbon and related non-graphene carbon allotropes.