When a triangle is translated, the lengths of its sides remain unchanged. This means that regardless of the translation (down 4 units and to the left 8 units in this case), the lengths of the sides of the triangle do not alter.
Since the length of side \( XY \) is 10 units, the length of the side \( X'Y' \) after the translation will also be 10 units.
Therefore, the length of side \( X'Y' \) is \( \boxed{10} \) units.