Under running water, wash the carrots and papaya. Cut the green papaya, carrots and garlic into small pieces. Use safety gloves if you're using a mandolin. Slice the green bell peppers very thinly with a knife.
Mix the green bell peppers, papaya, carrots and salt in a bowl. Let stand on the counter for 30 minutes to let the brine set.
Place the vegetables in a strainer. Run it under cold water to rinse. Next, place the vegetables on a cheesecloth.
To remove excess water, squeeze and wring out the vegetables from the cheesecloth.
Fill four sterilized 12 oz glass containers with the vegetables evenly.
Combine the sugar, vinegar, salt, and garlic in a small saucepan. Bring to a boil.
Reduce the heat to medium and continue cooking for one minute more until the sugar has dissolved.
Pour the liquid in the glass jars until it covers the vegetables. Mix the liquid with a chopstick. Cover the lid and let the jar come to room temperature before storing in the refrigerator.
Before you eat, let it rest for at least 2 days.