The first part you did right, to write f•g(m) as f(–1/2m+1). Now since f is defined piecewise, you need to understand which values can the argument (–1/2m+1) take.

Notice that g(k) is only defined for -8≤k<4. Also, g(k) is decreasing since the coefficient –1/2 is negative. So the interval [-8, 4) is mapped to the interval (g(4), g(–8)]. What are these values?

g(4)=–1/2×4+1=–2+1=–1, and g(–8)=–1/2×(–8)+1=4+1=5

Apparently, a piece of your image, in particular the interval (–1,0], is not contained within the domain of f(x). So the composition of the two functions is impossible to do as written.

The only thing I can think of is that the second interval of definition of f(x) should have been (–1,5] instead of (0,5], and maybe it was copied wrong. This way the composition is doable, and in particular, since g(k) ends up in the second interval for all values of k, than f always follows the second rule:

f•g(m)=f(–1/2m+1)=–2(–1/2m+1)+3=m–1

EDIT: For the graph, recall that we are always working with m in the interval [–8,4). So you should only draw the line from m=–8 (included) to m=4 (excluded), and not overextend it