As the non custodial parent with a 8332 form, how do i file my taxes. Do i mark my son lived with me all year?i know the father will be getting the earn income credit

[Hal_Al]

No.
Nothing about the number of months the child lived with you is sent to the IRS. That question is only asked so that TurboTax  can determine what  tax attributes you are allowed to claim. As the non-custodial parent, your answer must be something less than 6. It doesn't matter whether you enter 0 or 5 or something in between. It is OK for the other parent to answer 12, since he is the custodial parent for tax purposes.
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For others reading this, the custodial parent does have to show on IRS Schedule EIC, when claiming the Earned Income Credit, how many months the child lived with him. Entering 7, 8, 9, 10, 11, or 12 will qualify him for EIC. In this situation, the child alternated between parents for the first 8 months of the year. So, the child lived with him all year. The custodial parent would not be lying to claim 12 months.

[macuser_22]

Right, but the cutoff is 6.  0-6 are all the same and 7-12 are the same.   0-6 are not *more* than half the year and 7-12 are all more than half the year which is what the tax law requires.   Entering 6 months is exactally half the year so it is not *more* than half, so 6 is treated the same as 0.

(If the child lived with one parent for 183 days (6 months plus a day) then round up to the next month and enter 7 so that is is *more* than half).