Not sure where to find this info on my W-2. This is the question I am being asked:"Enter portion of Ohio adjusted gross income that is subjected to tax by another state

Look at Boxes 15-19 on your W-2.

On the line for Ohio, did they take out state taxes (Box 17), or just local taxes (Box 19)?

You should not be on that page. That is only for Ohio residents. 

Your employer should know better than to withhold Ohio STATE tax. There should be nothing in box 17 of your W-2 (on the line with OH in box 15).  If there is withholding  only in box 19, you do not need to file an OH return. 

Ohio has a reciprocal agreement, on wages, with all neighboring states. No Ohio state taxes are withheld or due and you do not need to file an OH return. But KYwill tax you on your Ohio income.

If Ohio STATE tax was mistakenly withheld, you have to file an Ohio return to get a refund. You should ask your employer to stop withholding so you don't have to file an Ohio return every year.

However the reciprocity agreement does not apply to local city taxes. You are not required to file a local city return, but you are also not entitled to a refund of the city withholding (box19 on your W-2), unless there was an error in the amount.

If you are subject to a KY county or city tax, you should check to see if the KY city will give you a credit for the OH city tax withheld. KY does allow an itemized deduction (Schedule A) for local tax paid.