Food Network teaches how to crush, slice and mince garlic. Peel off some of the papery skin from the garlic and then smash the head of garlic with the heel of your hand to loosen the cloves; if you only need a few cloves, leave the head intact and pull some off. Separate the cloves. To peel a clove, cut away the root end with your knife. Lay the flat side of the knife over the clove while holding the knife handle, then with the heel of your free hand carefully whack the knife against the garlic to separate the skin from the clove. To crush the peeled garlic, lay the flat side of the knife over the clove and smash it again. To slice peeled garlic, lay the clove flat on the cutting board and hold it with the fingertips of one hand, keeping them curled under. Using a rocking motion with the knife, make thin slices by moving the knife slowly across the clove. To mince peeled garlic, lay the flat side of a knife over the clove and smash it. Roughly chop the clove then move your free hand flat across the tip of the knife and use a rocking motion to chop the garlic until it’s finely minced.
Roughly chop the cucumbers, bell peppers, tomatoes, and red onions into 1-inch cubes. Put each vegetable separately into a food processor fitted with a steel blade and pulse until it is coarsely chopped. Do not overprocess!
After each vegetable is processed, combine them in a large bowl and add the garlic, tomato juice, vinegar, olive oil, salt, and pepper. Mix well and chill before serving. The longer gazpacho sits, the more the flavors develop.