There are actually two separate things going on here:
1) Exemptions - each person gets $x worth of income before any tax is owed at all. Roughly, this depends on your family size (there are many other nuances). This sounds like your $6,000 rule.
2) Deductions -- these are allowable expenses (business expenses, charitable contributions, certain types of interest, and so on). You can either keep records and claim the actual amount (which sounds like your system), or you can take the "standard deduction", which is the IRS's estimate of the amount of expenses an average person might have. The advantages of the standard deduction are that you don't have to keep records, and the standard deduction may actually be more than your real expenses if you don't have a lot of them.
1) Exemptions - each person gets $x worth of income before any tax is owed at all. Roughly, this depends on your family size (there are many other nuances). This sounds like your $6,000 rule. 2) Deductions -- these are allowable expenses (business expenses, charitable contributions, certain types of interest, and so on). You can either keep records and claim the actual amount (which sounds like your system), or you can take the "standard deduction", which is the IRS's estimate of the amount of expenses an average person might have. The advantages of the standard deduction are that you don't have to keep records, and the standard deduction may actually be more than your real expenses if you don't have a lot of them.