Add the distilled vinegar, water, kosher salt, and sugar to a large pot on the stove.
Heat until the kosher salt and sugar is dissolved.
Turn off heat and let this brine sit until it comes to room temperature.
While the brine is cooling, slice garlic cloves and add to bottom of mason jars. If you like spicy pickles, I'd suggest one whole clove per jar. If you like the garlic flavor but not the spice, then add just ½ clove to each jar.
Also add a few "stalks" of dill to each jar.
Then cut your cucumbers and place in jars. You can pack the cucumbers semi-full in the jars because when you pour the brine in that will fill the spaces and make the cucumbers "float" a little.
Pour the brine over the cucumbers in each jar making sure to completely cover all the cucumbers!
Cover and place in refrigerator for one week before eating. These will stay good in the fridge for 6-8 weeks!