Always read the context
@Some Beggar: "Here is Augustine on the age of the universe: 'They are deceived, too, by those highly mendacious documents which profess to give the history of many thousand years, though, reckoning by the sacred writings, we find that not 6000 years have yet passed.' "
If you read the context of that quote, you will find he is talking about the recorded history of man. Many sceptics laughed at the creation account, holding that the world - and man - had no beginning. The idea that the universe had a starting point was absurd to them - how could there be no universe, and where would it arise from? Speaking of the human race, Augustine quotes Apulieus thus, "Individually they are mortal, but collectively, and as a race, they are immortal."
Augustine then questions why the recorded history of man is so paltry if it extends to the infinite past. Surely they would have reached this point before? He gives other examples of historical records ranging up to 8000 years, but questions their consistency. Based on any of these records, however, he asserted that it points to a finite past.
He goes on to illustrate that any length of time less than infinity is vanishingly small by comparison, and therefore the questions and difficulties remain the same even if, "five or six, but even sixty or six hundred thousand years, or sixty times as many, or six hundred, or six hundred thousand times as many, or this sum multiplied until it could no longer be expressed in numbers, the same question could still be put..." At what point man came into existence beyond the creation of the universe was unanswerable to him, nor did he see it as of great significance.; "I own that I do not know what ages passed before the human race was created..."
You will also note that he refers to the "reckoning" of scripture, a reckoning being an estimate or calculation. He - and others - say this because there are no absolute time references to be found. Those who want to know more than the fact that God made the world have sought a means to work it out. They did this using genealogies in scripture, estimating the time between successive generations and assuming that when it was said that, "so-and-so was the son of such-and-such", they meant that there was only a single generation between them. Given that we have no idea when each generation was born, that it wasn't unusual for a distant descendent to be referred to as a "son" (even a man today could - in the proper use of the expression - be called "the son of Adam"), or that generations might be omitted from the series, how much weight do you think they gave to the resultant figure?
Augustine used this estimate as a benchmark in his assertion that the world (and man) had a beginning, and that is was a finite number of years. Scriptural records were as good a historical reference as any, and he used this to question why an eternity of mankind had not amounted to more. So judge for yourself - is 6000 years an assertion of scripture, or an extrapolation/calculation/estimate/reckoning derived from it? Add the fact that Augustine did not see the "days" of Genesis as a 24-hour period, or that he did not know what time elapsed before mankind, and you cannot claim that he was committed to any such number, or that it was pivotal to his faith. It was simply a (controversial) subject that fascinated him, and he explored it as deeply as he was able; "no matter at what earlier or later period he had been created, this controversy about the commencement of this world's history would have had precisely the same difficulties as it has now."