The stem and leaf plot is a way to plot data, allowing people to do a fast counting of a set of data.
As said in the key, 8|2 means 82, then to find how many people scored 78, we need to look for the "7" row and count how many "8" are there.
In the "7", which is the second row, there are 4 "8".
That means that 4 students scored 78.