You understand that the integral **is** the 'area under the curve' don't you? Here, since much of the graph is below the x-axis, that is really 'the area above the x-axis minus the area below the x-axis'.

Estimate those two areas by estimating what part of each square is in the region. Each square is 4 by 4 so has area 16. On the left, above the x-axis, I see, for x between -12 and 0 and y between 0 and 4, one full square, with a little more than half of the squares to the left and right of it. That would add to "two full squares" or 2(16)= 32. But the graph rises a little above that- I would estimate, for x between -12 and 0 and y larger than 4, about 1/2 of a full square so an additional 8. Do the same for the region on the right, below the x-axis, and subtract..

(You do understand that "estimate" means you aren't expected to give an exact answer, don't you?)