|Yes, those are all craters on the moon.|
...happened in just 6,000 years. We see craters like these on most solid bodies in our solar system, but for the sake of simplicity let's focus just on lunar craters for now. These craters demonstrate that our world is old in two ways. First, there's the evidence from sheer numbers. There are an estimated 300,000 craters larger than 1 kilometer on the near side of the moon alone—and the far side actually has significantly more. Based on the rate of such impacts, they must have taken place over hundreds of millions of years.
Then there's the evidence from big craters. The largest confirmed crater in the solar system is the massive South Pole–Aitken Basin, which is shown in dark blue on the right of the picture above. It measures an astonishing 2500 km (1600 mi) across. That's equal to the distance from San Diego to Memphis, from Dallas to Boston, or from Paris to Moscow. Had an impact of this caliber occurred while humans were alive, its effects would surely have been visible from earth, so why is there no mention of it in the historical record?
In addition, some craters on earth are also quite large, although tectonic activity makes them harder to find. The Chicxulub crater on the coast of Mexico is over 180 km (110 mi) across, and may have been responsible for the extinction of the dinosaurs. This impact would have resulted in worldwide earthquakes, wildfires, volcanic eruptions and kilometers-high tsunamis, filled the atmosphere with thick dust and broiled the planet’s surface. And that's not even the biggest crater. The largest one known, the Vredefort crater in South Africa (at right), is nearly 300 km (180 mi) across, so its effects would probably have been significantly worse. If impacts like these all occurred in the last few thousand years, isn't it strange that we have no human record for any of them?
There's not much YECs can do to effectively respond to these facts. Here's how Henry Morris, the father of modern creationism, tried to explain lunar craters in his book The Remarkable Birth of Planet Earth:
That's right, folks. The man largely responsible responsible for popularizing creationism in 20th century America believed that craters on the moon may have been caused by an outer space battle between angels and demons.
"[T]he possibility is at least open that the fractures and scars on the moon and Mars, the shattered remnants of an erstwhile planet that became the asteroids, the peculiar rings of Saturn, the meteorite swarms, and other such features that somehow seem alien to a "very good" universe as God must have created it may have been acquired later. Perhaps they reflect some kind of heavenly catastrophe associated either with Satan's primeval rebellion or his continuing battle against Michael and his angels."
Nowadays, YECs make the (only slightly less silly) claim that these impacts, while caused by real asteroids, were made during Creation Week, the Fall or the Flood. What they always conveniently fail to mention, however, is why. They could argue that the impacts on earth might be some form of divine punishment. But what possible reason could God have for hurling asteroids at the moon and even distant planets? Such actions would not have affected us in any way.
The truth is that most believers in a young earth never even consider the implications of phenomena as simple and obvious as impact craters. The few that do can only offer explanations that are both ridiculous and inadequate, letting their faith fill in the rest.