Quantity A: $\(|(x+y+z)|\)$
This is the absolute value of the sum of the three numbers.

Quantity B: $\(|x|+|y|+|z|\)$
This is the sum of the absolute values of the three numbers.

When are they equal?

The two quantities are equal when $x, y$, and $z$ are all non-negative (zero or positive) OR when they are all non-positive (zero or negative). In other words, when they all have the same sign (or are zero).

- Example 1 (All Positive):

- Let $\(x=2, y=3, z=4\)$.
- Quantity A: $\(|2+3+4|=|9|=9\)$
- Quantity B: $\(|2|+|3|+|4|=2+3+4=9\)$
- Result: $\(\mathrm{A}=\mathrm{B}\)$

- Example 2 (All Negative):

- Let $x=-2, y=-3, z=-4$.
- Quantity A: $\(|-2+(-3)+(-4)|=|-9|=9\)$
- Quantity B: $\(|-2|+|-3|+|-4|=2+3+4=9\)$
- Result: $\(\mathrm{A}=\mathrm{B}\)$

When is Quantity B Greater?

Quantity A is strictly less than Quantity B when $x, y$, and $z$ include at least one mix of positive and negative numbers (since the negative numbers will partially cancel out in the sum, but the absolute values will not).
- Example 3 (Mixed Signs):

- Let $\(x=10, y=-3, z=-4\)$.
- Quantity A: $\(|10+(-3)+(-4)|=|10-7|=|3|=3\)$
- Quantity B: $\(|10|+|-3|+|-4|=10+3+4=17\)$
- Result: $\(\mathrm{B}>\mathrm{A}\)$

Since the relationship between the two quantities changes depending on the signs of $x, y$ and $z$, the answer must be that the relationship cannot be determined.

Conclusion
The relationship cannot be determined from the information given.
Therefore, the correct answer is (D).