tax on property appreciation of 4 years.

The cost basis of the inherited property is the fair market value of the property at the time of the death. 

So if the property is sold not long after death, there would be little or no tax.

In your case, the death was four years ago, so there might be some appreciation for those 4 years, and you are only responsible for US capital gain tax based on the gains made in the 4 years after your father died.