Answer:
[tex]\huge\boxed{f(x)=-2x-8\ \text{or}\ f(x)=2x+\dfrac{8}{3}}[/tex]
Step-by-step explanation:
[tex]f(x)=ax+b\\\\(f\circ f)(x)=a(ax+b)+b=a^2x+ab+b\\\\(f\circ f)(x)=4x+8\\\Downarrow\\a^2x+ab+b=4x+8\Rightarrow a^2=4\ \wedge\ ab+b=8\\\\a^2=4\to a=\pm\sqrt4\to a=\pm2\\\\\text{for}\ a=-2:\\-2b+b=8\\-b=8\\\boxed{b=-8}\\\\\text{for}\ a=2:\\2b+b=8\\3b=8\\\boxed{b=\frac{8}{3}}[/tex]
