The most appropriate approach for designing the CI/CD pipeline for the given scenario would be to use Google Cloud Build to create separate pipelines for front-end and back-end. Here’s why this approach is the best choice:

• Flexibility: Google Cloud Build provides flexibility to create separate pipelines for different components of the application, allowing for independent development, testing, and deployment.
• Scalability: Google Cloud Build can handle large and complex projects, scaling up or down resources as needed.
• Integration: It integrates seamlessly with other Google Cloud Platform services, making it easy to manage the entire application lifecycle.
• Efficiency: By creating separate pipelines, you can optimize the build and test processes for each component, improving overall efficiency.

While other options might be possible, they have certain drawbacks:

• Using Jenkins with separate pipelines: This approach can be more complex to manage and maintain, especially if the project grows large.
• Using Google Cloud Build and Cloud Run with a single pipeline: While this approach can simplify the deployment process, it might not be as efficient for large and complex applications.
• Using Kubernetes Engine and Jenkins with a single pipeline: This approach can be more complex and resource-intensive, especially for smaller projects.

Therefore, using Google Cloud Build with separate pipelines for the front-end and back-end is the most recommended approach for the given scenario.