Sterilize jars and keep hot, after my jars are sterilized I put them in my oven at 200 degree to keep them hot, then take them out in batches of 6 pints per recipe batch, it will all depend on how much cabbage mix you put in your jars.
Pack cabbage mixture in hot jars, tight but NOT like a brick. Then dip and pour syrup over cabbage mixture, use a chopstick by sticking down through to remove air bubbles and distribute liquid then add more liquid if needed leaving 1/2 inch head space.
Wipe jar rim with vinegar/water paper towel to remove sticky residue from liquid and get proper seal. Screw bands finger tight.
Place in water Bath with 3 Tablespoons of white vinegar added to the canning water(the white vinegar helps prevent the white residue on the jars after canning), make sure water is warm but not too hot since your brine/syrup is not hot, it is just room temperature. If water is too hot it will crack your jars.
Make sure water covers top of jars and lids by at least 1to 2 inches I prefer 2 inches
After water comes to a boil in canner with cole slaw jars,time, process 15 minutes then turn off heat under canner, take canner lid off and let cole slaw jars sit in canner 10 minutes before taking out of the canner. Place on towel on counter or table out of draft until the jars have sealed. After 24 hours remove rings and wash jars in mild luke warm sink of water, I also use a Tiny amount of Dawn dish soap and white vinegar in my washing water then rinse with clear water and dry, dropping jar rings in the washing water wash, rinse and dry rings for next time.
Store jars without the rings if lid pops off then discard contents.