I sold a rental house and used the money to pay off another rental house. How can I offset the capital gains?

[MichaelL1]

You can't offset the gain by paying off another rental property.

There is a provision for a like-kind exchange but this is not a like-kind exchange.  That is when you buy sell one property and a 3rd party holds the money until your purchase closes a like-kind property. 

The sale of the rental property must be reported on the return. It does not matter for tax purposes what you did with the money, however paying down debt is always a great idea.