Answer
The sorted list is $\{1,2,3,4,5,6\}$. Please check the solution to see how the algorithm arrives at this solution.
Work Step by Step
The binary insertion sort is characterized by finding the next index using a binary search algorithm. The sort main loop occurs $n-1$ times (from $2$ to $n$) and for each iteration $i$, the proper index of $a_i$ is found in the previous terms $a_1$ to $a_{i-1}$.
In this example, the list is $\{3,2,4,5,1,6\}$
For the first iteration, the binary search is called on the mini-set $\{3\}$ with target $:=2$. The index returned is $1$ and hence $2$ is moved to that index giving us $\{2,3,4,5,1,6\}$.
For the second iteration, the binary search is called on the mini-set $\{2, 3\}$ with target $:=4$. The index returned is $3$ and hence no change is done to the list.
For the third iteration, the binary search is called on the mini-set $\{2, 3, 4\}$ with target $:=5$. The index returned is $4$ and hence no change is done to the list.
For the fourth iteration, the binary search is called on the mini-set $\{2, 3, 4, 5\}$ with target $:=1$. The index returned is $1$ and hence $1$ $\it crawls$ to that location, shifting everything else one space to the right giving us $\{1,2,3,4,5,6\}$.
For the third iteration, the binary search is called on the mini-set $\{1, 2, 3, 4, 5\}$ with target $:=6$. The index returned is $6$ and hence no change is done to the list.
