Pack the carrots, daikon radish, cucumber, and jalapeno (if using) into a 500ml (16oz) jar. If you have more room in your jar, just matchstick up a bit more veg and add it to the jar so that it is full.
Stir all the pickling liquid ingredients together in a measuring cup or (another vessel that is easy to pour from) until the sugar and salt are dissolved. Pour over the veggies until the jar is filled to the top. If you have leftover pickling liquid, just discard it. Let the veggies pickle for as little as 15 minutes before using, or store covered in the fridge for over a week.