Tennessee doesn't have state taxes . But these two w2's are making me out a state in that field . What do I do ?

 If your state is not listed it doesn't have an income tax.  Leave W2 boxes 15,16, & 17 BLANK, empty, no spaces. 

Did you leave the entire state section blank or did you enter 0's or anything at all?  If you entered 0 please go back and delete the 0's and then this should let you leave the state name blank. 

If you live and work in TN, then you can enter TN as the state for your W2 if it is insisting and you have no 0's in the state section.  When it comes time to do the state taxes, simply skip and continue to file your return.  You can choose just to file a federal return.