"how this YEC claim gets around the ample evidence (geological and other) that the world, the solar system and the Universe) is very old and that it is only 6,000 years young"

Ed - it's all to do with Einsteinian Time Dilation. Unless you just ignore that claims of 'older than 6,000'

After all

2 Peter 3:8 New International Version
"With the Lord a day is like a thousand years, and a thousand years are like a day. "

Don't ask me, mate, I'm not a believer in this stuff... after all, it's 'beyond all human understanding'....