If the nine-digit number 43x1145y2 is divisible by 88, then the value of (3x — 2y), for the smallest value of y, is:

43x1145y2
Now 88=8*11
so it will be divisible by 8 and 11
Now we will check for 8

for checking divisiblity of 8 . the last three digit of a number must be divisible by 8.

5y2 should be divisible by 8 or
so we get y=1 or 5 or 9
Now y=1 (smallest)
Now for 11 : 
2 + 5 + 1 + x + 4 - (1 + 4 + 1 + 3) = 11k (multiple of 11)
we get 3 + x  = 11k
we get k = 1
The possible of x = 8 
so 3x  -2y = 24 - 2 = 22 

Hence , Option D is correct.