Acceleration versus time graph of a particle starting from rest and moving along a straight line is as shown. The displacement after 20 s is

For 0<t<10, it is having constant acceleration of 4ms^-2 and zero initial velocity. 

for 10<t<18, it is moving with a constant velocity of 40ms^-1.

for 18<t<20, it is moving with a acceleration of -4ms^-2 and initial velocity of 40ms^-1.

$\mathrm{S}=\left[\frac{1}{2}\times 4\times {10}^2\right]+\left[(4\times 10)\times 8\right]+\left[40\times 2+\frac{1}{2}(-4)2^2\right]$

$=(200+400-8)\mathrm{m}=592\mathrm{m}$