The length of a side of a triangle does not change when the triangle is translated. Translation preserves the shape and size of the triangle, simply moving it to a different location in the coordinate plane.
In this case, since triangle \( XYZ \) is translated down 4 units and to the left 8 units, the length of side \( XY \) will remain the same after the translation.
Given that the length of side \( XY \) is 10 units, the length of side \( X'Y' \) (the translated side) will also be:
\[ \text{Length of } X'Y' = 10 \text{ units} \]
So, the length of side \( X'Y' \) is 10 units.