Spin- 12 chains with alternating antiferromagnetic (AF) and ferromagnetic (FM) couplings exhibit quantum entanglement as the integer-spin Haldane chains and might be similarly utilized for quantum computations. Such alternating AF-FM chains have been proposed to be realized in the distorted honeycomb lattice compound Na2Cu2TeO6 , but to confirm this picture a comprehensive understanding of the exchange interactions including terms outside of the idealized model is required. Here, we employ neutron scattering to study the spin dynamics in Na2Cu2TeO6 and accurately determine the coupling strengths through the random phase approximation and density functional theory approaches. We find the AF and FM intrachain couplings are the dominant terms in the spin Hamiltonian, while the interchain couplings are AF but perturbative. This hierarchy in the coupling strengths and the alternating signs of the intrachain couplings can be understood through their different exchange paths. Our results establish Na2Cu2TeO6 as a weakly coupled alternating AF-FM chain compound and reveal the robustness of the gapped ground state in alternating chains under weak interchain couplings.