Before discussing the evidence for a young Earth, it is necessary to show that this is what the Bible really teaches. There are those who try to squeeze the billions of years claimed by evolutionists in to the firstchapter of Genesis. Are any of these views consistent with what the Bible actually says?
One method called the gap theory assumes that there was a gap between Genesis 1:1 and Genesis 1:2. The problem with this view is that there is no place in the Bible ware such a gap is mentioned. They usually try to put Satan's fall in this Gap, but the Bible makes it clear that Satan's fall took place no earlier than day 6.
Ezekiel 28:13. Thou hast been in Eden the garden of God; every precious stone was thy covering, the sardius, topaz, and the diamond, the Beryl, the onyx, and the jasper, the sapphire, the emerald, and the carbuncle, and gold: the workmanship of thy tabrets and of thy pipes was prepared in thee in the day that thou wast created.
14. Thou art the anointed cherub that covereth; and I have set thee so: thou wast upon the holy mountain of God; thou hast walked up and down in the midst of the stones of fire.
15. Thou wast perfect in thy ways from the day that thou wast created, till iniquity was found in thee.
It clearly says that Satan was in the Garden of Eden before he fell and the according to Genesis 2 tthe Garden of Eden was created on the same day as Adam, which was day 6.
The Day age and progressive creation theories try to make the days of creation something other than 6 ordinary days. The problem is that according to Genesis 1 the Earth and the Universe were all created in 6, literal Earth days. This fact is demonstrated by "and the evening and the morning were the nth day." This is clearly a reference to an ordinary day night cycle. They will also claim that while the Hebrew word yom can mean a literal day, that it can also mean an indefinite period of time, the problem with this is that yom always means ordinary days when used with a number. When included with the " evening and morning " reference there can be no other interpretation other than 6 literal Earth days.
This is further supported by Exodus 20:9-11:
Exodus 20:9. Six days shalt thou labour, and do all thy work:
10. But the seventh day is the sabbath of the Lord thy God: in it thou shalt not do any work, thou, nor thy son, nor thy daughter, thy manservant, nor thy maidservant, nor thy cattle, nor thy stranger that is within thy gates:
11. For in six days the Lord made heaven and earth, the sea, and all that in them is, and rested the seventh day: wherefore the Lord blessed the sabbath day, and hallowed it.
Here God clearly commands the Israelites to work 6 days and rest on the 7th. It also show that this principle to be a commemoration of the 6 days of creation with God resting on the 7th. The days between Sabbaths are unquestionably 6 literal Earth days, the connection support the fact that creation was 6 literal Earth days.
To determine the Biblical age of the Earth it is nesesary to find an event that has an established date and then use Biblical references to calculate from there. The destruction of the Temple in Jerusalem by Nebuchadnezzar is often used. The next step is calculating the time between this event and abraham's birth. Here disagreements in how to interpret certain passages can lead to some variation but the variation is not more than few hundred years.
Calculating the time between Abraham, and creation relies on the ages of the father at the birth of the listed son; as give in the genealogies in Genesis 5 and 11. These ages are added up and then added to the time of Abraham's birth. Now there is some dispute about how old Terah (Abraham's Father) was when Abraham was born. Terah was ether 70 or 130 when Abraham was born but since the difference is only 60 years it is within the margin of error for other historical dates.
The resulting age of the Earth is 6000 to 6400 years. This is the bases of Usher's date for creation of 4004 B.C. He started with a 4 B.C. date for the birth of Christ. The English Old Testament; regardless of the version; was translated from Masoretic Text. However there are other texts that have variations in some of the ages of the genealogies in Genesis 5 and 1.1
The most well known of these texts are the Septuagint. It is the Greek translation of the paleo-Hebrew text; called the Vorlage. The tranlation dates to about 250 BC. Both Masoretic Text and Samaritan Pentateuch are also from this text. The Septuagint is 350 years older than the Masoretic text.
The differences between the Septuagint and Masoretic text chronology is systematic enough to show that it does not result from a random error. While its generally excepted that it is the Septuagint that is in error, because of evidence of revision in other places, it is still useful in setting an upward limit one the Biblical age of the Earth.
Based on the Septuagint Alexndrinus, the age of the Earth would be 7300 - 7800 years old. If one uses the Samaritan Pentateuch the age is 6300 - 6700 years. This places Biblical age of the Earth and Universe at 6,000 - 8,000 years. The real point is that if you take the Biblical account at face value, you can only get an age of a few thousand years for the age of the Earth.
Special note: There are two versions of the Septuagint; the Alexndrinus and Vaticanus. The Vaticanus has a reduced pre flood chronology resulting in Methuselah dying after the Flood. This has led to a general criticism of the Septuagint chronology, however the Alexndrinus does not have this problem, so this argument is not valid against it.