Following are the steps to follow to solve Tower of Hanoi problem recursively.
Let the three pegs be A, B and C. The goal is to move n pegs from A to C.
To move n discs from peg A to peg C:
move n-1 discs from A to B. This leaves disc n alone on peg A
move disc n from A to C
move n?1 discs from B to C so they sit on disc n
The recurrence function T(n) for time complexity of the above recursive solution can be written as following.
T(n) = 2T(n-1) + 1, Hence D is the right answer.