If one node is present at extreme left side of the leaves and other node at the other extreme right side of the leaves ,then these two nodes have to cover up height 2 times .From extreme left to root and then from root to Extreme right .
Height of Binary tree$= \log_{2}n$
so Answer is $= \log_{2}n$ + $ \log_{2}n$ =$2 \log_{2}n$