Light and moisture are garlic’s worst enemies, as they both cause mold to grow.
BRAIDS: Braids should be hung in a well ventilated dry dark place out of direct sunlight.
BULBS: Store garlic bulbs at room temperature in a dry, dark place that has plenty of air circulation, like in a wire-mesh basket or open paper bag in a cupboard or pantry.
If you have old stockings, drop a bulb in the toe, tie a knot above it, drop in another bulb, tie another knot, and so on until you fill up the stocking, and hang it in a well-ventilated dry dark place.
Another thing to try: use old cardboard egg cartons. Do not use plastic cartons. Place a bulb in each section, and store in a dark, cool dry place.