Fog computing is developed to complement cloud computing by extending the cloud services (computing, storage, networking, and management) to the edge of the network in order to reduce service latency. With the rapid growth of cloud users and the emergence of fog computing, the demand for cloud/fog resources has increased dramatically. Also, the incremental use of the cloud/fog resources and their applications has increased energy consumption and carbon emitted, which caused significant environmental challenges. Optimizing the placement of requested applications (e.g., in the form of virtual machines) is one of the main solutions, which has a primary effect in reducing the energy consumption of cloud/fog architecture and consequently their carbon emissions. However, due to the geographic distribution of cloud and fog data centers, there is a variety of carbon emission levels to consider, which makes optimizing the placement of applications in distributed cloud/fog more challenging than in centralized clouds in terms of carbon efficiency. In this paper, we propose a multi-level approach using a mixed-integer linear programming (MILP) model to minimize carbon emissions (CO2) by optimizing the usage of cloud/fog resources. These resources are managed by virtual machines (VMs), which can be optimally and virtually used. In our model, we used the British Telecom (BT) as a telecom network example with an aim to minimize the CO2 emission, considering several scenarios of traffic demand during different times of the day and year (seasons). The results show that the optimal location to host applications highly relies on the carbon intensity and traffic demands. The results also show there is a trade-off between CO2 emission reduced by shortening network journey, and CO2 increased by hosting more applications into the fog nodes. In addition, the results demonstrate that the proposed green fog-cloud architecture outperforms the central cloud and the distributed clouds in terms of reducing the total CO2 emission by up to 91% and 71%, respectively. Finally, we develop a heuristic algorithm to mimic and validate the presented work, and it shows comparable results to the MILP model.INDEX TERMS Cloud computing, fog computing, green fog-cloud architecture, applications placement, energy-efficiency, carbon emissions CO2.