Best way to think of this is as follows....
In most economies we have inflation, which as we know - refers to increasing prices. If I earn $100 in one year, and $100 in the next, despite the fact that I am still earning the same income; my purchasing power has decreased, as prices rise under inflation. So I might have been able to purchase 100 cans of softdrink in year one, whereas in year two i might only be able to purchase 90.
This is what we mean by real Vs nominal (or money) gdp. Nominal gdp simply refers to GDP in its amount irrespective of price rises. Real GDP however, scales nominal gdp down, so that it takes into account the rise in prices (so that you can appropriately compare the two GDP figures on an even playing field).
In order to calculate real GDP, we need to "weight" or "scale" nominal GDP based on relative prices - that is prices in year one, compared to prices in year two. The CPI is a tool we use to describe the price level in a given year (based on a basket of goods). So in order to calculate real GDP, we multiply nominal gdp by the ratio of prices between the two years.
In this case, we use the following:
CPI Year 1 / CPI Year 3 = 100 / 125 = 0.8
This is a number that reflects the rise in prices. In other words, $1 of currency now, can buy what $0.8 could in year 1. This reflects inflation.
In order to calculate real GDP, we need to multiple this number (reflecting relative prices) by nominal GDP:
0.8 x 820 = $656
This real income ($656) can be directly compared to the base year's nominal income (i.e. 600). So we can say there has been a rise in real gdp as of course 656 > 600. However, we cannot compare it directly to years 2 and 4 as we only know nominal GDP for these years. We would need to do the same thing (multiply nominal income by relative prices) for these years in order to make a fair comparison.
The final point to make, is that the question has asked you to use the base year. In this case, you would use year 1. The base year simply refers to the year you are comparing it to. Because the CPI for year one is 100 we know that this is the base year. Any year could be the base year. For example year 1 might be 90, year 2 might be 100, and year 3 might be 115. In this case year 2 is the base year with the CPI for years 1 and 3 being measured relative to year 2 (which is 100).