Using identity = ( x+y )^2 = x^2 + 2xy +y^2
= (12)^2 = x^2 + 64 + y^2
= 144 = x^2 + y^2 + 64
144 - 64 = x^2 + y^2
80 = x^2 + y^2
The answer is x^2 + y^2 = 80.

**Given Information:**

We are given two equations:
1. xy = 12 (equation 1)
2. xy = 32 (equation 2)

We need to find the value of x^2y^2.

**Solution:**

To find the value of x^2y^2, we need to simplify the expression using the given information.

From equation 1, we can express x in terms of y:
x = 12/y

Substituting this value of x in equation 2, we get:
(12/y)y = 32

Simplifying the equation, we have:
12 = 32y/y

Cancelling out the y terms, we get:
12 = 32

But this is not true, which means there is no solution that satisfies both equations simultaneously.

Therefore, we cannot find a specific value for x^2y^2 using the given information.

**Conclusion:**

The value of x^2y^2 cannot be determined using the given equations.