I am trying to ask my human res. Here at my job this question but it seems like I am getting brushed off all the time I do not want to be penalized at the end of the year I have been working in this job since march of 2006 we just switched payroll and I get direct dep. So I never bothered looking at my stubs something told me to look I realized that for 2 months they were taking taxes out for NJ not for PA where I live I know that before we switched payroll the checks showed both PA ANd NJ taxes taken out my question is what happens to the 2 months that I did not pay PA taxes because of my payrolls mistake and what is the exact taxes that are suppose to come out of my check from pA and NJ please some one help me

The exact amount depends upon your total income picture. They have withholding tables to determine the amounts based upon your income earned at the job and the number of withholding allowances you claim on your W4.
Ultimately it is your job to determine how many allowances to claim.
Do you have your taxes prepared by someone or do you do them yourself?
If you have them prepared, you could get help with your W4 and/or state withholding documents.
You will have to pay tax on the amount you earn to NJ, but you will get a tax credit for what you pay to NJ on your PA return. If the PA rate is higher, you will owe additional to PA, but if NJ is higher, you will not owe any more to PA which means the months with no withholding will not cause a problem.
Looking at the tables, it looks like NJ goes to a higher rate, depending upon how much you earn.
Hope this helps.

DLC summarizes it rather well. I have nothing to add.