In a pot over medium-high heat, add vinegars and sugar to the pot and stir until sugar is dissolved.
1 cup white vinegar, ½ cup apple cider vinegar, ¼ cup granulated sugar
In the meantime, toss cabbage and carrots together then pack into large mason jars or whatever canning jar you use.
½ head of small green cabbage, 2 carrots
When the liquid is ready, carefully pour into the mason jars, covering the cabbage and carrot mixture.
Close the lid and allow the mixture to cool to room temperature then put in the refrigerator and allow it to get better over time! You may eat it after 30 minutes though, too!
Notes
If you have a larger head of cabbage, you may find you need to make a second batch of brining liquid.