Cut the vegetables coarse or fine, there's no right or wrong way, just your preference. If you like less heat, discard the seeds and membranes from the jalapenos.
½ head cabbage, 2 large carrots, 2 medium jalapenos, 1 large onion
Toss the vegetables to mix them so they are evenly distributed.
Fill the jars with the chopped vegetables to 1" below the rim, packing them down as you go.
Heat your sauce pan on medium high, with no oil. Dry fry the whole cumin seeds and coriander seeds for a minute or two.
½ teaspoon cumin, ½ teaspoon coriander
Add the vinegar, water, salt, sugar, and garlic to the sauce pan and bring to a boil.
1½ cup vinegar, ½ cup water, 1 teaspoon salt, 1 tablespoon sugar, 3 cloves garlic
Simmer the brine on low for 5 minutes so that the garlic slivers are cooked completely.
Place the sealing lids and screw on rims (or sealing clips) on the jars while hot. As they cool, the jars will create a vacuum.
When the Mexican pickled vegetables are cooled, store in the refrigerator. Wait until chilled before serving.