We are given that $\(w, x\)$, and $y$ are consecutive even integers and that their product $\(w x y=\)$ 0 . For a product of numbers to be zero, at least one of the numbers must be zero.

Given $\(w<x<y\)$, let's look at the three possible scenarios where one of these even integers is zero:

Scenario 1: $\(y=0\)$
If $y$ is the zero, then the consecutive even integers preceding it are:
- $y=0$
- $x=-2$
- $w=-4$
- In this case, Quantity \($\mathbf{A}(x=-2)\)$ is less than Quantity $\(\mathbf{B}(0)\)$.

Scenario 2: $x=0$
If $x$ is the zero, the set is:
- $y=2$
- $x=0$
- $w=-2$
- In this case, Quantity A ( $x=0$ ) is equal to Quantity B ( 0 ).

Scenario 3: $w=0$
If $w$ is the zero, the set is:
- $y=4$
- $x=2$
- $w=0$
- In this case, Quantity A( $\(x=2\)$ ) is greater than Quantity B ( 0 ).

Conclusion
Because $x$ could be $-2,0$, or 2 depending on which of the three integers is the zero, we have three different possible relationships ( $\(<,=,>\)$ ).

The correct answer is $\(\mathbf{D}\)$ : The relationship cannot be determined from the information given.