Multinational manufacturing organisations face significant challenges in achieving environmental sustainability objectives due to various operational, geographical, social, and economic challenges. This study presents a scoping review and bibliometric analysis that investigates engineering problem-solving methods and techniques that can be applied towards achieving these objectives. Adopting the JBI method and PRISMA-ScR framework, 69 studies were selected through a systematic search of the Web of Science database. The bibliometric analysis revealed a growing research interest in engineering-based sustainability approaches, particularly within the themes of green manufacturing, lean six sigma, and life cycle assessment. Collaboration among countries such as the United Kingdom, India, the USA, and China is notable, while the adoption of digital technologies remains limited. This review synthesizes current knowledge and identifies key gaps, particularly around the integration of Industry 4.0 technologies, and proposes the Green Lean Six Sigma (GLSS) family of frameworks as a promising foundation for environmental sustainability. The findings lay the groundwork for developing an integrated engineering framework to address environmental sustainability objectives in multinational manufacturing organisations.