The goat is tied to two poles with ropes that are 15-metre long, has access to an area denoted by a circle with the pole as the center and the length of the rope as the radius. Therefore, the grazing area around each pole is a circular region with a 15-metre radius.

Option 1: This only includes the area within the reach of one pole, thus excluding the second pole. Therefore, it`s not the complete grazing area.

Option 2: The goat can reach the full 15-metre radius from both poles P and Q, this overflowing in some areas where the circles overlap, and creating a sort of figure-eight (8) shape. This covers the most ground for the goat, so this is the correct answer.

Option 3: Though this area overlaps the two poles, the total combined overlap does not make up a complete circle from either pole, thus providing less grazing area than needed.

Option 4: While covering the entire 15-metre radius from either pole, it excludes the overlapping area. Thus, it is smaller than the total reachable area.