Wash jars in warm, soapy water. Place the washed jars in a deep pot or canner. Fill the jars up to the top and the canner up to the same level as the jars with water. Cover the canner and bring water to a simmer (with small bubbles).

Wash lids and bands with warm soapy water. Drop them into the canner together with the jars. When ready to use, take them out from the canner with a pair of tongs. Dry them with a clean towel.

Peel daikon with a vegetable peeler. Then cut into matchsticks 1/8 inch think and 3 inches long. Do the same for the carrots. Place in a large bowl and mix them up.

Divide matchstick daikon and carrot equally between the 2 prepared quart sized mason jars.

Combine rice vinegar, water, sugar, and salt in a small saucepan. Bring to a boil and stir until sugar and salt have dissolved completely.

Pour hot brine into jars to cover matchstick daikon and carrot completely. Press down daikon and carrots with a ladle if necessary. Seal jars with lids and bands.

Allow brine to cool. Transfer to the refrigerator.

Pickled daikon and carrot are ready to eat after 2 or 3 days. Store in refrigerator submerged in brine and consume within 2 months.