Trim green beans into 4-inch pieces. Pack beans lengthwise into 4 hot 1-pint canning jars, leaving 1/2-inch head space. To each jar, add 1/4 teaspoon cayenne pepper, 1 dill stem (or 1 teaspoon dill seed), and 1 garlic clove. In a medium-size saucepan, bring remaining ingredients to a boil. Pour boiling liquid over beans, leaving 1/2-inch head space. Run a hot knife along the inside of the jar to remove air bubbles. Wipe jar rims. Seal tightly. Process 40 minutes in a boiling-water bath (for canning and safety instructions, see the link below). Remove and cool. You'll hear the lids "pop" when they seal. Let beans stand at least two weeks before tasting to let the flavor develop.