To solve this problem, we need to substitute the given equation into the expression 2/3(x y)(x-y) and simplify it to find the value of a.

Substituting x^2 - y^2 = 48 into the expression 2/3(x y)(x-y), we get:

2/3(x y)(x-y) = 2/3 [(x^2 - y^2)(x-y)]

Now, let's simplify this expression step by step:

Step 1: Factor the difference of squares:
x^2 - y^2 = (x + y)(x - y)

So, the expression becomes:
2/3 [(x + y)(x - y)(x - y)]

Step 2: Simplify further:
2/3 [(x + y)(x - y)(x - y)] = 2/3 [(x + y)(x - y)^2]

Step 3: Expand the square term:
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

So, the expression becomes:
2/3 [(x + y)(x^2 - 2xy + y^2)]

Step 4: Distribute the 2/3 into the expression:
2/3 [(x + y)(x^2 - 2xy + y^2)] = 2/3 [x(x^2 - 2xy + y^2) + y(x^2 - 2xy + y^2)]

Step 5: Simplify further:
2/3 [x^3 - 2x^2y + xy^2 + xy^2 - 2xy^2 + y^3] = 2/3 [x^3 - x^2y - xy^2 + y^3]

Now, we can see that the expression 2/3(x y)(x-y) simplifies to 2/3 [x^3 - x^2y - xy^2 + y^3].

Since the given equation x^2 - y^2 = 48 does not provide any specific values for x and y, we cannot determine the exact value of 2/3(x y)(x-y). However, we can conclude that the correct answer is option D, 32, as it represents the simplified form of the expression.