$f(g(x))=8 x^{2}-2 x$ $$ g(f(x))=4 x^{2}+6 x+1 $$

let $f(x)=c x^{2}+d x+e$

$g(x)=a x+b$

$f(g(x))=c(a x+b)^{2}+d(a x+b)+e \equiv 8 x^{2}-2 x$

$g(f(x))=a\left(c x^{2}+d x+e\right)+b \equiv 4 x^{2}+6 x+1$

$\therefore \quad a c=4 \quad a d=6 \quad a e+b=1$

$a^{2} c=8 \quad 2 a b c+a d=-2 \quad c b^{2}+b d+e=0$

By solving

$a=2 \quad b=-1$

$c=2 \quad d=3 \quad e=1$

$\therefore \quad f(x)=2 x^{2}+3 x+1$

$g(x)=2 x-1$

$f(2)+g(2)=2(2)^{2}+3(2)+1+2(2)-1$

$=18$