Problem:
What is the smallest possible value for the product of 2 real numbers that differ by 6?

Solution:
To find the smallest possible value for the product of two real numbers that differ by 6, let's consider two scenarios: one where the numbers are positive and another where the numbers are negative.

Positive Numbers:
Let the two numbers be x and y such that x > y. Since the numbers differ by 6, we have:
x - y = 6
Rearranging the equation, we get:
x = y + 6
Now, we need to minimize the product xy. Substituting the value of x in terms of y, we have:
xy = (y + 6)y = y^2 + 6y
Since y^2 and 6y are both positive for positive values of y, the product xy will be positive as well. Therefore, the smallest possible value for the product xy cannot be 0.

Negative Numbers:
Now let's consider the scenario where both x and y are negative numbers. In this case, we still have x - y = 6, but since both numbers are negative, the difference will be negative as well. So, let's rewrite the equation as:
y - x = 6
Rearranging, we get:
x = y - 6
Substituting the value of x in terms of y, we have:
xy = (y - 6)y = y^2 - 6y
Since y^2 is always non-negative and -6y is always non-positive for negative values of y, the product xy will be non-positive. Therefore, the smallest possible value for the product xy can be 0 or any negative number.

Conclusion:
From the analysis above, we can conclude that the smallest possible value for the product of two real numbers that differ by 6 is 0. Therefore, the correct answer is option 'D' (0).