f is the function -2x+6, g is the function x+2.
We want the area below both functions, so the system will feature a "less than" sign in both inequalities.
In particular, the graph of g is included in the shaded area, whereas the graph of f is not included.
This means that, in particular, the inequality involving f will have a strict sign (<), and the inequality for g will have a "less than or equal to" sign (
).