"I had moving expenses that I incurred that I paid off before my job refunded me for the expenses"
If you were reimbursed for your moving expenses, then they are not deductible in Arkansas, UNLESS you were taxed on the reimbursement. Did your employer (if one) add the reimbursement to Wages in box 1?
"If I put the amount of the moving expenses my return goes up if I put 0 my return goes down. "
You mean your "refund" goes up or down; your "return" is the document you are sending to the IRS or the state.
There are many reasons your refund may go up or down, and since we can't see your private tax data, we can't tell you why. However, note that it is not a good idea to watch the Refund Mete too closely, because TurboTax is making calculations in the background that are out of sync with what you are doing.
Wait until you finish entering the Arkansas input and then go look at your form AR1000ADJ and see if your moving expenses are listed there on line 8. If they are, you are OK.
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