There's a key piece of information that we have to assume about this problem: that there is a 100% probability of hitting the game board. (you will definitely hit the board). That means the probability of getting into the hole is the area of the hole divided by the area of the board.
The area of the board is given: 44 in²
The area of the hole is 3x3 = 9 in²
The probability of hitting the hole on any given try:
9/44
Twice in a row:
9/44 * 9/44 = 81/1936
Answer is B) 81/1936