So although I did believe in the gap theory for a little while, I guess I'm an "old-young" earther when I say 50,000 to 100,000 years. That allows for science telling us that the origins of humans or certain cultures are about 100,000 years or whatever it is, and is not so large as to discredit a 7 day literal creation.
I think 4.5 billion years is absolutely rediculous and unfathomable. I also think the methods at arriving to a 6000 year conclusion are incredibly naive and lacks understanding of a) biblical genealogies and b) biblical timelines and c) numerical symbolism.
6000 years is arrived at simply by adding up the numbers of ages in the bible. Anyone with a calculator can do it. There's a few problems with this method though. For one, the bible is not a complete genealogical record (there are gaps) and secondly is not meant to be a genealogical record of the whole human race but rather focusses on the Hebrews and Israel as might be expected. Thirdly, we need to use the same timescale as the bible uses. The Hebrews had a calender system in which they divided the period of daylight into 12 parts (I think, as far as I remember). Some days would be 14 hours long, others 9 hours long, depending on how much sunlight they had. Our time scale is different. 1 year elapsing in the old testament is not the same as our 365 day years. Using the same naive methods that 6000-year theorists use in biblical interpretation, we could also easily arrive at a flat-earth and geocentric universe conclusion. Good for back in the day when they didn't know much about science - not so good for us today if we want to try and win converts. The Australian aboriginal culture alone is worked out to go back 40,000 or so years. That's why I think a 50,000 to 100,000 years or so figure is ball-park.
Any argument for 6000 years may also be made coming from a prophetic timeline perspective or by dividing the human history into nice equal parts of 6 or 7. This has merit but is also naive. Firstly, prophetic timelines are not chronoligically accurate. Secondly, whenever we see whole numbers, particularly 6's , 7's, 3's etc and multiples of , the first thing to think is symbolism! Suppose that each set of 1000 years in God's symbolic timescale of a 7000 year symbolic creation is equal to 2000 literal years in our calender. That easily comes to a 12,000 literal year age of the earth. The thing is, there is nothing in the bible to say we can infer literal chronological time-scales from biblical symbolism. These same methods which fall short in predicting the future return of the Messiah, also fall short when used in reverse to predict the age of the earth.