A is the correct answer, as generating a destructivechanges.xml file and deploying the package via the Force.com Migration Tool is the best way to manage the deletions of metadata components across sandbox environments and production with minimal impact on other work streams. A destructivechanges.xml file is a special file that specifies the components to be deleted from an org, and can be deployed using the Force.com Migration Tool, which is a command-line tool that uses the Metadata API to retrieve and deploy metadata components. This method can help to automate and streamline the deletion process, as well as ensure consistency and accuracy across the environments. B is incorrect, as performing deletes manually in a sandbox and then deploying a change set to production is not a good way to manage the deletions, as it can introduce errors and inconsistencies, as well as require additional steps and permissions. C is incorrect, as assigning business analysts to perform the deletes and splitting up the work between them is not a good way to manage the deletions, as it can create confusion and complexity, as well as lack of coordination and integration. D is incorrect, as deleting the components in production and then refreshing all sandboxes to receive the changes is not a good way to manage the deletions, as it can disrupt the production environment and the ongoing development and testing activities in the sandboxes. You can learn more about this topic in the Deploy Changes with the Force.com Migration Tool unit on Trailhead.