Line breaks aren't working for you because the formatting in the answers isn't implemented for the question field (hint hint, powers that be).
As usual I'm going to be very general here because I am not a scientist, but I will try to include key points you can google later.
The number one method young-Earth creationists use to make a young earth plausible in light of geological and paleontological realities is to exploit the most catastrophic world-changing event in the Bible set chronologically between Creation and Armageddon: Noah's flood. This is the raison d'etre of so-called flood geology.
The flood, they claim, carved out the Grand Canyon, wiped out all of the animals we only see today as fossils, and laid down all the strata in quick succession as sediment.
To put it mildly, there are a multitude of potential problems with this.
One is the rigid position of all animals worldwide in the strata. In the chaos of a planet overwhelmed by rushing water, why are all specimens in a given extinct species (say, trilobites) found in the same layer instead of all over the place?
There's one clever explanation that simple animals were drowned first, followed by successively more advanced animals who could fly or were more agile. So the higher they are the longer they held on, and the more evolved they "appear". However you'd expect millions of exceptions to this, for example a small reptile holding onto a floating log. There are many claims of objects found out of sequence, like petrified trees penetrating many strata, but no proven anomalies yet.
Radiocarbon dating is the most straightforward method of disproving the young earth. Using basic laws of nuclear physics, it regularly establishes the age of objects as tens of thousands to millions of years old. Even one such object would prove the earth to be least that old, but this happens all the dang time.
Therefore, of course, there's a huge effort by creationists to discredit radiocarbon dating completely and utterly. There are large margins of error sometimes, but when you're only trying to make sure something is older than six millennia, an error of millions of years out of greater millions hardly matters.
What many don't know is that there are many different forms of dating, based in principle on the initial carbon method but using other particles. Some of these have indeed been found unreliable and are no longer in use (and are publicised by some creationists to represent the whole field as a failure) but this does not reflect upon the methods still used.
Similar to this geological argument between young-earth creationists and everybody else is the astronomical argument. There are objects greater than 6000 light years away, such that if the universe were that young, light from them wouldn't have reached us yet.
One creationist has developed a bigger cousin to flood geology, namely white hole cosmology. WHC assigns different time speeds to different areas, so that six thousand years here is billions of years at the edge of the universe. Besides WHC, there are other ideas involving light moving faster than the speed of light itself. Needless to say, these ideas as applied in this way are without support in mainstream science.
The first thing I'd throw at them in your situation, Healy, is those distant objects in space. White hole cosmology isn't nearly as well-rehearsed as flood geology, and the responses tend to sound really cool in a sci-fi B-movie sort of way. It might be fun. Either that, or they might concede an old universe and concentrate on a young Earth, which is not a very stable position.