Preparation Place cabbage in large bowl. Add vinegar and sugar; toss to coat. Cover and let stand 30 minutes. Toss cabbage mixture well; cover and let stand 30 minutes longer. Drain cabbage. DO AHEAD: Can be made 8 hours ahead. Cover and chill. Transfer drained cabbage to another large bowl. Add carrots, green onions, and mayonnaise; toss to coat. Season to taste with salt and pepper.
Preparation Place cabbage in large bowl. Add vinegar and sugar; toss to coat. Cover and let stand 30 minutes. Toss cabbage mixture well; cover and let stand 30 minutes longer. Drain cabbage. DO AHEAD: Can be made 8 hours ahead. Cover and chill. Transfer drained cabbage to another large bowl. Add carrots, green onions, and mayonnaise; toss to coat. Season to taste with salt and pepper.