I owe an additional $2,400 to NY State, can that additional tax be deducted off of 2016 Federal, it will be paid 4/18/2017

[DoninGA]

State taxes paid after 12/31/2016 cannot be deducted on a 2016 federal tax return Form 1040 Schedule A.  You can deduct the state taxes paid in 2017 on your 2017 tax return next year.