Well, the figure seems to report that velocity is measured in m/s²... That label should say m/s. (Unless of course this is the graph of acceleration over time, but then the answer would probably be more complicated than the given choices.)
If the graph indeed shows velocity, and the unit is just a typo, then the displacement from A to D is equal to the area under the curve.
From A to B, the area is of a triangle with height 4 m/s and base 1 s, hence the area is 1/2 • (4 m/s) • (1 s) = 2 m.
From B to C, it's a rectangle with length 3 s and height 4 m/s, hence with area (3 s) • (4 m/s) = 12 m.
From C to D, it's a trapezoid with "height" 2 s and bases 4 m/s and 2 m/s, hence with area 1/2 • (4 m/s + 2 m/s) • (2 s) = 6 m.
The total displacement is then 2 m + 12 m + 6m = 20 m.
