You’ll mix food coloring with water at two different temperatures. measure and pour ½ cup of hot water from the faucet into a glass. then measure and pour ½ cup of cold water from the faucet into the other glass. hold the dropper of food coloring just above the surface of the water, and carefully add one drop in the center of each glass. wait a few minutes and then look at the glasses from the side. place the white piece of paper behind the glasses to make it easier to see. what do you observe? is there a difference in how it mixes?

Looks like you're learning about diffusion.
Diffusion is the net movement of molecules down their concentration gradient (high to low concentration).

The dye inside the dye bottle contains 100% concentration of dye.

If you put the dye in hot water, the dye would spread, or diffuse, pretty fast throughout the water, from its high concentration to low concentration. This is because hot water increases the energy of the molecules, causing them to move fast in random directions. The hot water would make both the dye molecules and water molecules move fast so the dye can diffuse in the water until it reaches equilibrium faster. You would see that all of the water is colored faster than the dye in cooler water.

Normal cool water would make the solution reach equilibrium slower than the hot water.

The answer to your question really depends on three things: how much water you have, how cold it is to start out, and how cold the things around it are. water actually freezes when it gets to 32 degrees fahrenheit (0 degrees celsius), but the time it takes to get there may be different.  let's start with the first. if you take two glasses, and fill one with a tiny bit of water, and the other about halfway, then put them both in the freezer, the one with less water will freeze first (you can try this at home, but i recommend using plastic cups and not glass ones).  now let's move on to the second part. let's say you have two glasses, and you fill one with really cold water that has been in the refrigerator, and the other with really hot water from the sink. if you put both of them in the freezer, the one that started out colder will freeze first.  for the third part, let's imagine that you have two glasses with the same amount of water in them, and the water is at the same temperature. imagine putting one outside on a really really cold day in georgia, and having a friend in alaska put one outside on the same day. since it would be so much colder in alaska, the glass of water there would freeze before yours.  so, if you took a tiny bit of really cold water in a glass, and put it outside on a cold day in alaska, it would freeze a lot faster than a big glass of hot water outside on a cold day in georgia. 

Iam pretty sure that the answer is d