You are given a graph that you can look at. You are asked to rank g'(-1), g'(8), g'(2), and g'(4) in increasing order.
What is "$\mathbf{g'(a)}$"?
It's the slope of the tangent to the graph through the point $\mathbf{(a,g(a))}$.
So: g'(-1) is the slope of the tangent to the graph you are looking at, through the point with $x$-coordinate $-1$. g'(8) is the slope of the tangent to the graph you are looking at through the point with $x$-coordinate $8$. g'(2) is the slope of the tangent through the point with $x$-coordinate $2$ of the graph you are looking at. g'(4) is the slope of the tangent to the graph you are looking at, through the point with $x$-coordinate $4$.
But they are numbers, because the "slope of the tangent" is itself a number.
Since you can see the graph, you can estimate what the tangent will look like graphically. Since you can estimate what the tangent will look like, you can see which tangent is steepest (has the largest slope), and which tangent has the smallest slope. Use those estimates to order the numbers g'(-1), g'(8), g'(2), and g'(4) in order.
The number $0$ would represent a tangent line with slope $0$, that is, horizontal. Positive slopes are lines that "rise" as you move left to right; negative slopes are lines that "fall" as you move left to right. Again: since you can see the graph, and you can estimate what the tangents will be, you should be able to figure out which tangents have positive slope (and go after the $0$ in the list you will give), and which ones have negative slope (and go before $0$ in the list you will give).
In short: This question (a typical question from many a calculus book) is asking you to use what the derivative represents (not how it is computed) to describe at which points the function whose graph you are seeing has steepest or flattest graph, where it is "decreasing rapidly", where it is decreasing but slower, where it is increasing a bit, and where it is increasing the fastest, and to place $0$ to separate the points where the graph has negative slope and where the graph has positive slope.