Mix 6 cups water and 6 Tbsp salt in a very large bowl, stirring to dissolve salt.
Place cabbage, cut side up, in water so that water almost covers the cabbage.
Put a heavy plate on top of cabbage, then top with something heavy (iron skillet, rock) to submerge the cabbage in the salt water.
Set aside at room temperature for 12 - 24 hours.
Drain cabbage; discard water.
Rinse cabbage well under cold water.
Mix 4 cups water, 1 Tbsp salt, sugar and fish sauce in the same bowl. Let brine stand until salt and sugar dissolve, stirring occasionally, about 10 minutes.
Mix pear, daikon, green onions, and garlic in medium bowl.
Lift each cabbage leaf and distribute some radish mixture between each leaf. It doesn't have to be perfect!
Nestle layered cabbage in the bowl of brine as tightly as possible.
Once all cabbage quarters are layered and place in the bowl, put a plate on top with weight, as before.
Set aside at room temperature. Note: if you're using the bowl recommended above, you shouldn't need to 'burp' it; however, if you end up putting in jars with lids, you will need to let the air out that's created by the fermentation. Try for twice a day, particularly at the start.
After 6 or 7 days, taste daily until you obtain the desired flavor. Note: fermentation depends on a lot of things, but the temperature is a big one. Fermentation will occur quickly if your house is warm and more slowly if your house is cool.
When ready, store in the refrigerator. You can transfer the cabbage and juices to lidded glass jars if you like. Note: always use glass, preferably with plastic caps or place a square of parchment paper under the lid if using a metal lid. Fermentation brine is very reactive.
When you're ready to serve, remove a full quarter of the cabbage. Place it on a work surface and cut crosswise into 1 to 1.5-inch slices.
Note: Fermentation will continue for as long as you have food for the healthy microbes to eat. However, putting your kimchi in the fridge will massively slow things down. Kimchi will keep a very long time (that's the point of fermentation) as long as you ensure the brine is always covering the cabbage.