Cook first 6 ingredients in a medium saucepan over medium-high heat about 4 to 6 minutes or until sugar is dissolved. Remove saucepan from stove, and cool mixture completely.
Snap off tough ends of asparagus.
Pack 1 bunch asparagus, 2 dill sprigs, and 1 garlic clove into 1 (1-quart) canning jar; repeat process with 2 remaining jars, asparagus, dill sprigs, and garlic cloves.
Pour vinegar mixture evenly into jars; seal jars. Chill at least 8 hours; store in refrigerator up to 1 week.