Preheat grill to 400° to 450° (high) heat. Spread butter on 1 side of 12 bread slices. Layer 2 white American cheese slices and 1 mild Cheddar cheese slice on unbuttered sides of each of 6 bread slices. Top with remaining bread slices, buttered sides up. Grill 1 to 2 minutes on each side or until grill marks appear and cheese melts.