To simplify the expression \((2/3x^2 - \frac{y}{2})(2/3x^2 + \frac{y}{2})(2/3x^2 - \frac{y}{2})(2/3x^2 + \frac{y}{2})\), we can first notice that the expression consists of two pairs of identical factors.

Let's denote:

\[
a = 2/3x^2
\]
\[
b = \frac{y}{2}
\]

Thus, the expression can be rewritten as:

\[
(a - b)(a + b)(a - b)(a + b)
\]

This can be simplified to:

\[
[(a - b)(a + b)]^2
\]

Now, we can use the difference of squares formula:

\[
(a - b)(a + b) = a^2 - b^2
\]

Now substituting back for \(a\) and \(b\):

\[
a^2 - b^2 = \left(2/3x^2\right)^2 - \left(\frac{y}{2}\right)^2
\]

Calculating \(a^2\) and \(b^2\):

\[
\left(2/3x^2\right)^2 = \frac{4}{9}x^4
\]
\[
\left(\frac{y}{2}\right)^2 = \frac{y^2}{4}
\]

Thus, we have:

\[
a^2 - b^2 = \frac{4}{9}x^4 - \frac{y^2}{4}
\]

Now substituting back into our expression:

\[
[(a - b)(a + b)]^2 = \left(\frac{4}{9}x^4 - \frac{y^2}{4}\right)^2
\]

Therefore, the simplified expression is:

\[
\left(\frac{4}{9}x^4 - \frac{y^2}{4}\right)^2
\]