Plumbing – repair this cold water hose

There will indeed be some type of rubber, silicone or other type of flexible materal washer thing inside the nut. The cross section picture below attempts to show how the typical compression fitting of this type works.

As the nut tightens it compresses the "rubber" part against the end of the threaded plastic piece and around the outside of the incoming water line. Leaks can arise as from this "rubber" part getting hard and inflexible. The chorine added to water can accelerate this this problem. Over tightening the compression nut will also lead to problems. Sometimes a corrosive build up on the water tube can also lead to leak issues. Usually it is combination of all three elements and everything is OK till there is some flexure in the joint and then it starts to leak.

To fix it is suggested to replace the compression nut and the "rubber" part. If the inlet tubing is corroded then clean it up with steel wool. If the plastic threaded part is stripped from previous over tightening then you will also have to replace the fill valve assembly in the tank too. You should be able to find replacement parts at hardware or home stores. Replacement parts are usually fairly reasonable in cost.

Check at a hardware store. They often sell a bag of faucet washers of a mix of sizes that can be used to repair your faucet. You pick out the one from the kit that suits your faucet.

Sometimes the hardware store will have a whole section of individual faucet repair parts. Take the faucet washer and stem seal with you to match them up with new parts.

On the other hand the garden faucets probably are available in only so many styles. You could take a picture of your existing leaky faucet and take it along with you to the hardware store or other big box type store and purchase a new one of the same or very similar style. Then take it apart to redeploy the rubber parts from it for use in your old faucet.

Added Information:

I have actually repaired a faucet that was an outdoor spigot type in a unique way. It's valve stem piece was very corroded and logically led to the conclusion to replace the whole faucet. Unfortunately I found that the faucet was soldered onto a pipe inside the wall behind a stucco exterior and no direct access from the inside of the wall either. I took a sharp focused picture of the faucet and traveled off to the big box store and happened to find a full new faucet that was identical in every way to the old faucet. I was able to re-use the stem, top portion of the faucet body and the packing nut from the new faucet on the old lower portion faucet body and restore to like new performance without having to break any stucco or tear down a blind inside wall.