I sold a house in 2019. I used the proceeds for a down payment on another home. Does this affect my return? Does it offset capital gains?

if you owned and lived in it for any 2 years in the 5 years before date of sale, if married your spouse must also have lived in it 2 out of 5 years,  you get a home sale exclusion $250,000 if single $500,000 if married and the test is met. if you took depreciation on the home, that's subject to recapture.  if you sold a personal residence at a gain in the two years before this sale the excludable gain is reduced.    

if this is a vaction home or other property not use for personal residence the gain is fully taxable 

TT should take you through all the questions that need answering in order to determine reportability. 

The old rule about using the proceeds to buy a new home was eliminated about 20 years ago.  The transactions are now completely separate.  You must determine your capital gains on the sale of the old home, and if your gain is more than your exclusion, you pay capital gains tax.