Think of this as plotting points on a coordinate graph.
In year 1, there were 100 people (x-value) who lived in an economy with $44,000 (y-value) as the real GDP. (100, 44000)
In year 2, there were 102 people (x-value) who lived in an economy with $47,200 (y-value) as the real GDP. (102, 47200)
The question asks to find the growth rate of the real GDP per capita, and "per capita" means "for each person". So we are asked to find the slope using these two coordinate points.
m = (y2 - y1)/(x2 - X1) = (47200-44000)/(102-100) = 3200/2 = 1600
The growth rate of the real GDP increased by $1,600 per capita.