How do Young Earth Creationists explain artifacts dated to 20,000 years ago or more? Many creationists and Christians believe the earth is around 6000 years old. I am taking art history and some of the artifacts or pieces of art that were created by humans back then had been carbon dated back to 10,000 to 20,000 years ago or even longer.

How do Young Earth Creationists explain this?
As others noted, icr.org and answersingenesis.com have numerous articles on the subject. The argument is usually boiled down into the following points:

1) Accurate radioactive dating assumes that the decay rate of a radioactive material has not changed over time and is the same today as long in the past.

2) Dating of objects less than about 50,000 years old is done using Carbon-14, not other isotopes that have much longer half-lives, such as potassium-argon, uranium-lead, rubidium-strontium, etc. (See http://www.creationstudies.org/operationsalt/carbon14.html ) (Other non-radioactive methods have their proponents, and these methods have their own problems. e.g. dendrochronology- studying tree rings. See http://www.icr.org/article/7058/ )

3) Only once-living things may be so dated. (Although, consider the presence of C-14 in diamonds thought to be millions or billions of years old: https://answersingenesis.org/geology/carbon-14/carbon-14-in-fossils-and-diamonds/ ) (Also, there are restrictions. e.g. Sea creatures and animals that eat sea creatures are excluded, since the amount of C-14 in the ocean is much different than the atmosphere.)

4) Dating using Carbon-14 assumes that the fraction of C-14 in the atmosphere had reached a steady state value long ago and has not changed appreciably since then. (C-14 is assumed to be created by cosmic rays hitting Nitrogen in the atmosphere.)

5) C-14 is absorbed into organisms via respiration or consuming plants that contain it.

6) After the organism dies and is buried, no more C-14 enters it, and the C-14 already inside it begins to decay, starting the clock.

7) During the period that the organism is buried and fossilized or preserved in some other way, no chemical processes cause additional C-14 to enter the specimen or be leached out of it.

8) When the specimen is dug up and prepared for analysis, it is not contaminated by foreign sources of carbon.

9) The machines used to determine the ratio of C-14 to C-12 are well-calibrated and sensitive enough to make an accurate determination.

I doubt that anyone, Creationist, Evolutionist or other, would disagree with what I just said. The question is, how valid are the many assumptions that I listed? Some of them must be taken on faith - we have no way to inspect the entire geological and chemical history that a specimen has undergone in order to tell if any assumptions have been violated.

Young earth creationists have challenged several of the assumptions.

1) If the Earth was recently created, then at the start, before any cosmic rays had yet hit the atmosphere, there would be no C-14 in it. Any plants or animals that died and were buried at this time would have no C-14, hence would appear to be very old - say 100,000 years old, or the limit of our machines ability to measure.

2) Over time, as C-14 built up in the atmosphere (via cosmic ray bombardment of atmospheric Nitrogen), things would begin to take on a younger C-14 age.

3) The flood of Noah removed a huge amount of carbon from the biosphere, burying it underground. This cause a sudden drop in C-14. (See https://www.icr.org/article/7311 )

4) Since then, C-14 has recovered and increased.

The above story is consistent with the Bible, and accounts for fluctuation in C-14 concentrations in the atmosphere that would then be interpreted as older and younger ages than the true ages.

In addition, experiments have been performed that show that the decay rate can be altered under certain laboratory conditions. (See https://answersingenesis.org/geology/radiometric-dating/acceleration-of-radioactivity-shown-in-laboratory/ )  It is theorized that the flood was caused by God speeding the decay rate, causing excess heat inside the earth, triggering volcanism and earthquakes and shifting tectonic plates, which poured steam into the atmosphere, forming the clouds that inundated the world.

The resulting warm ocean and volcanoes caused so much water and dust to enter the atmosphere, that they blocked the sun and triggered an ice age. (See http://www.icr.org/article/ice-age-genesis-flood/ )

The importance of understanding the true initial conditions of the earth cannot be overstated. For example, potassium-argon dating (used for longer time scales) assumes that molten volcanic rock is so hot that it forces all the argon gas out before the rock cools. Then inside the cool rock, potassium begins to decay into argon, which remains trapped in the solid rock. However, recent volcanoes have been studied. Volcanic rocks only a year or two old are found to be millions of years old by K-Ar dating, because they have argon gas that the theories said should not be there. Thus we have actual experimental evidence to show that their assumptions are not (at least in some cases) valid. (See https://answersingenesis.org/geology/radiometric-dating/anomalous-potassium-argon-ages-implications/ )

Quote from http://www.creationstudies.org/operationsalt/carbon14.html: 


  "Scientists now realize that production of carbon-14 has not been
  constant over the years, but has changed as the radiation from the sun
  has fluctuated."