Till December 6 i was working in Georgia and now i am working in Texas location so while filling the tax do i need to mentioned about my movement and what about state tax

[MarilynG1]

If you were a Georgia Resident in 2019, file a Resident Return to Georgia, reporting all your 2019 income.

Normally, you would file a Non-Resident tax return to the state you worked in (but did not live in).  However, since Texas has no State Tax, you don't need to file a return to report your earnings there.

Click the link for more info on filing multiple states.