If my ex-husband owes over 4,000 in back child support but haven't files taxes in over 6 years what could happen?

You could file a contempt of court for failure to pay child support.

You can file a contempt of order motion in court. You should probably consult a family law attorney in your area.

He is forfeiting the right to any refund once three years past the due date of the return expires. He is also running the risk that the IRS will file a substitute return for him, and then collect the tax based on that return. I would also not be surprised if he is flagged in the offset program, which would seize any refund he is due.

If the court had ordered him to pay, he must follow through with the order, or be held in court. You can file a motion holding him in contempt for failing to abide by such an order. Good luck.