You will need 7 pint jars (or 3 quarts and 1 pint), preferably wide-mouthed. Into each pint jar, put 1/2 a jalapeno pepper, 2 whole cloves, 1/2 tsp. crushed red pepper, and one clove of crushed garlic.
Start a large canning pot so that it is boiling and ready when the carrots are all packed into jars. Be sure to start with adequate water to completely submerge the jars by about an inch. Put the lids and rings in a small saucepan and bring to a simmer; turn off heat and let lids/rings remain in the hot water until you need them.
Peel and trim both ends off the carrots. Cut them into carrot sticks that are one inch shorter than the pint jars. Pack the carrots sticks upright in the jars and fairly tightly. Put odd lengths and bits of carrots into one jar so the rest of them are as uniform as possible. (Or, if you have large carrots, you might like them cut into diagonal round slices.)
In a large pot, mix the vinegars, sugar and salt. Heat to boiling, stirring to dissolve sugar and salt. Carefully pour the hot vinegar into the jars over the packed carrots, leaving 1/2-inch headspace. (You might have extra vinegar if you did a nice job packing the carrots tightly.) Wipe the rims of the jars with a damp paper towel. At this point, if you aren’t canning these, add lids and put your refrigerator pickles in the refrigerator. Eat within four months.
For canning: Add lids and rings and process in the boiling water bath for 15 minutes (20 for quarts). Then, turn off the heat and let the jars sit in the bath for an additional 5 minutes before removing to the counter (onto a dish towel). Let sit un-disturbed for 24 hours. Check seals. If any jars failed to seal, store in the fridge. Otherwise, store in a cool, dark place for up at a year.