1. Combine water, salt and sugar in a saucepan.
2. Place over medium heat and stir until the salt and sugar crystals dissolve.
3. Bring to a boil, then pour in the vinegar and after a minute turn off the heat.
4. Place an equal amount of mustard seeds, peppercorns and coriander seeds into the sterilized jars.
5. Fill the jars with sliced banana peppers leaving 1" of head space.
6. Using the funnel, pour the hot brine mixture over the peppers. The brine should completely cover the peppers.
7. Use a butter knife to jostle the peppers in the jar and release air bubbles.
8. Peel the garlic from the husk, cut it into slices and add to the jars.
9. Wipe the rim of the jars with a damp paper towel.
10. Cover the jars with sterilized lids and tighten with rings.
11. Process the jars, covered with boiling water, in a water bath canner for 20 minutes.
12. Carefully remove the jars from the canner and set on a tea towel to cool to room temperature.
13. When the snap lids have "popped" the pickled peppers may be stored in a cool dark place for up to 2 years.