If the slope of line DE = the slope of line BC, then DE is parallel to BC.
D is the midpoint of AB, so D = (4+22,6−22) = (3, 2)
E is the midpoint of AC, so E = (4−22,6−42) = (1, 1)
slope of DE = y2−y1x2−x1=2−13−1=12
slope of BC = y2−y1x2−x1=−4+2−2−2=−2−4=12
Since the slope of DE and the slope of BC both equal 12 , DE is parallel to BC.
Here's a graph to check: https://www.desmos.com/calculator/5k2mf7pbjj