Step-by-step explanation:
If DE and BC are parallel, then they have the same slope.
We have
A(4, 6), B(2, -2), C(-2, -4)
The formula of a midpoint:

D is the midpoint of AB, and E is a midpoint of AC.
Calculate the coordinateso fo D and E:

The formula of a slope:

Calculate the formula of a DE and BC:

The slope DE and the slope BC are the same.
Therefore DE is parallel to BC.