What they call a “problem” is a strength. The earlier dates they cite were all developed by studying and publishing the evidence; the revised dates came about because other scientists examined the evidence and challenged it by acquiring more date and better tools.
Only a simple-minded fool would consider clinging to an old idea in the face of new evidence to be a virtue. Show me reasonable evidence that the current dates are wrong, and I’ll accept that. So that’s what AiG should do, right? Show us the evidence that the Earth is only 6,000 years old? Here it comes!
Furthermore, a great deal of evidence [Get ready to start counting their evidence!] exists that is perfectly consistent with the notion that dinosaurs and humans lived together. First and foremost, the  Bible states that man and all land animals were both created on Day Six. Since dinosaurs were primarily land animals, this means man and dinosaurs lived at the same time. Also,  Job was told to consider the behemoth (Job 40:15–24), a creature whose description seems to match that of a sauropod dinosaur. In addition to the biblical testimony, we have discovered  pictographs, petroglyphs, and brass carvings of dinosaurs,  soft tissue and red blood cells in a tyrannosaur femur, as well as records from cultures around the globe of  dinosaur-like creatures (often called dragons). There are even some reports that  some dinosaurs may still be alive, though we need to be careful to verify such reports.
So the  eyewitness testimony (God’s Word) tells us that earth is about 6,000 years old, and He is most certainly a reliable witness. In fact, it is  impossible for Him to lie (Titus 1:2; Hebrews 6:18). Also, the historical data is perfectly consistent with the idea that the earth is young and that dinosaurs and man have lived together.