Not sure how to approach this or how to answer it

You approach this by identifying the line that bounds the shaded area and the side of the line the shaded area represents.

The line that has positive slope has a slope of 1 (it goes 1 square up for 1 square to the right), and it has a y-intercept of -2. Thus its equation is
  y = x - 2

The shaded area is below this solid line, so corresponds to the solution to
  y ≤ x - 2

Only one answer selection includes this inequality—the last one. You answer this by making the selection of that system of inequalities.
  y ≤ x - 2
  y ≤ -3x -6


Had there been more choices that included the inequality we found, you would then look at the other line. It has a slope of -3 (down 3 squares for each square to the right) and it intersects the y-axis at y = -6. Thus its equation is
  y = -3x - 6

Again, the shaded area is below the line (y values are less than those defined by the line), so the shaded area corresponds to the solution of
  y ≤ -3x - 6

Now, you have both of the inequalities in the system of inequalities. The shaded area is the area that belongs to the solution sets of both of them.