There are a few ways to go about this, I think the most obvious is the one I outline below:
x = C(:,1);
y = C(:,2);
cond_1 = x > 0 & x < 5 & y < 6;
cond_2 = x > 5 & x < 12 & y < 3*x + 6;
cond_3 = x > 12 & x < 15 & y < -3*x + 7;
cond_4 = x > 15 & x < 20 & y < 6;
points_below = C(cond_1 | cond_2 | cond_3 | cond_4, 1:2)
The method above assumes the array is called C. I redefine the columns into variables. I then use conditional statements that select for points matching the conditions above. NOTE: You may want to review the conditions you have in place, as they seem a bit strange to me, and maybe not what you are intending for.
However, the above should provide you with the final set of points as shown in the array points_below. Conditional statements are very powerful in Matlab.