Their website was out-of-date and they were having some infrastructure issues (some "basic" packages versions, like PHP, were old as well), and they weren't able to properly 'use' their website. They first asked us to solve those problems, before migrating to a newer Drupal.
We recommended that they migrate their site content and functionality to Drupal 8, and to move to different hosting (AWS). We also recommended that this project be managed in two phases.
Phase 1 would focus on providing small bug fixes for their legacy Drupal 6 website and completing some discovery work on what it would take to migrate to Drupal 8.
Phase 2 would be migrating their Drupal 6 website to Drupal 8. We then estimated the effort and tried to determine possible roadblocks.