If I live in the state of Texas,decided to move back home to Georgia.Can I file my taxes in Georgia r do I have to file in Texas?

You file taxes based on where you are living at the time. If you live in GA, you file a state income tax return with GA. If you live in TX... well, Texas has no income tax so you don't have to file with TX at all. When you move from TX to GA you will have to pay GA income tax on income received starting from the date you move into the state.