A 3d array defined as a[2][2][2] means that there are 2 2d arrays each of dimension 2x2, i.e., both of them have 2 rows and 2 columns.
Suppose the array given in the question is A[x][y][z]. This means that there are x 2d arrays each having y rows and z columns.
In the questions, the equations for finding A[i][j][k] can be re written in the form of y and z as follows if the array is assumed to be of type 'int':-
t0 = i ∗ 1024 = i * (y*z) * 4
t1 = j ∗ 32 = j * z * 4
t2 = k ∗ 4 = k * 4
So from the above equations we get,
z*4=32
=> z=8
and y*z*4=1024
=> y=32
So we know that dimensions are A[x][32][8]. Since we assumed int, so A is the answer since it is of this form.
If you assume array to be char then,
t0 = i ∗ 1024 = i * (y*z) * 1
t1 = j ∗ 32 = j * z * 1
t2 = k ∗ 4 = k * 4
So from the above equations we get,
z*1=32
=> z=32
and y*z*1=1024
=> y=32
So none of the char options,i.e, options B and C are of the form A[x][32][32]. So A has to be the answer.