Combine mayonnaise, sour cream, and garlic in a small bowl. This will be the dressing.
Cut a medium purple cabbage into 4 equal wedges. Then slice the core off of each wedge. Slice each each wedge into thin strips.
Place the sliced cabbage into a large bowl. Add the chopped pecans, dill, salt, pepper, and dressing. Combine until all the ingredients are well incorporated.