I am planning to root some grocery store edible field mint (with most leaves removed and bottom and top cut) in 3 and 4 inch plastic pots. My question is, is keeping them in 2 hours of direct sunlight okay? Or should they be kept in complete shade? Last time the ones planted in 12 inch pots with 6 hours direct sunlight did very well but the 2 hour ones dried up. I don't have transparent glass tumblers for rooting in water.
The fundamental problem all cuttings have is sufficient water uptake. As long as the cuttings don’t have roots, you need to keep evaporation trough the leaves to a minimum.
That’s why you shouldn’t place them in direct sunlight. Dappled shade is good because it’ll give a good balance between light for photosynthesis and less evaporation. Initially covering the cuttings with something transparent to create a mini greenhouse can also help. An inverted glass container, a cut-off plastic bottle, a sheet of cling wrap can all be a makeshift cover. Under that, you get a high humidity atmosphere that minimizes losses in the cuttings. At least once a day you should lift up the cover to give the plants a bit of fresh air and prevent mold. Now, I am not saying that it’s impossible to place the new cuttings in direct sun, some will be fine (as you observed), but overall, I would not recommend it.
For mint, I would rather stick fresh twigs in water than directly into soil, as discussed in the other Q/A.