a) If $g∘(2f)=f+h$ where $f(x)=2x + 5$ and $h(x)=x^3 -2x$
b) If $(2f)∘g=f+h$ where $f(x)=\ln(x+2)$ and $h(x)=\sin(x^2)$
(a) Write out $f+h$ (that you can do directly). Then write out $2f$. Then try to expresss $f+h$ in terms of $2f$. Your expression is what $g$ does.
For example, if we have $f(x) = 3x+1$ and $h(x) = 36x^2+21x+3$, then $f+h = 36x^2 + 24x+4$. On the other hand, $2f = 6x+2$. Can we write $f+h$ in terms of $2f$? Yes: $(6x+2)^2 = 36x^2 + 24x + 4$, so $g(u) = u^2$ would satisfy $g\circ(2f)=f+h$.
(b) Similar to (a), but now you are doing $(2f)\circ g$ with the given $f$ and $h$.
In short: Write it out, figure it out.