Whisk together sugar and vinegar until sugar dissolves. Stir in red pepper and garlic; cover and let stand 4 hours.
Cook green beans and carrot in boiling water 1 minute; drain. Plunge into ice water to stop cooking process; drain.
Pour vinegar mixture over vegetables, tossing to coat. Let stand 1 hour before serving.
Makes: 4 to 6. Servings: