Wash 4-pint size jars and lids in hot soapy water; rinse with hot water; keep jars warm until needed.
In a small stainless steel or enamel saucepan, heat the vinegar, water, sugar, and salt over medium-high heat. Stir until the sugar melts; the brine should change from cloudy to clear with no salt or sugar in the bottom of the saucepan. Turn off the heat.
Meanwhile, fill a water process canner or (a pot large pot) with enough water to cover jars with 1-inch of water; bring water to boil.
Place 1 smashed garlic clove in a hot jar, and pack jar tightly with the jalapeno slices, leaving 1⁄2-inch headspace. Using a canning funnel, ladle the hot pickling liquid over the jalapenos, again leaving 1⁄2-inch headspace. Remove air bubbles with the headspace tool. Wipe jar rim clean, center the lid on the jar and secure the band to just fingertip-tight. Place jar in boiling-water canner. Repeat until all jars are filled.
Process jars by returning the water to a boil. Process for 10 minutes. Turn off heat; remove the lid, and let the jars remain inside the canning pot for at least 5 minutes. Remove jars from the canning pot. Cool, undisturbed for at least 12 hours.
Store in a cool, dark place. Good for up to 1 year.
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