Introduction:
We are given that a, b, c, and d are integers, and we need to find the minimum possible value of the expression (a-b)² * (a-c)² * (a-d)².

Approach:
To find the minimum value of the given expression, we need to analyze the factors that contribute to its value. Let's break down the expression into its constituent parts and analyze each one separately.

Analysis:

1. (a-b)²:
This term represents the square of the difference between a and b. The square of any number is always positive, so (a-b)² will also be positive. Therefore, this term does not affect the minimum value of the expression.

2. (a-c)²:
Similar to the previous term, (a-c)² represents the square of the difference between a and c. As the square of any number is always positive, this term also does not affect the minimum value of the expression.

3. (a-d)²:
Again, (a-d)² represents the square of the difference between a and d. Like the previous terms, this term is always positive and does not contribute to the minimum value.

Conclusion:
From the analysis above, we can conclude that all the terms in the given expression are always positive. Therefore, the minimum possible value of the expression is 0, which occurs when a = b = c = d.

However, it is important to note that the given statement "a b c d" is not clear. It seems to imply that a, b, c, and d are distinct integers, but the question does not explicitly state this assumption. If a, b, c, and d can be equal, then the minimum value of the expression is 0. If they must be distinct integers, then the minimum value cannot be determined as it depends on the specific values of a, b, c, and d.