Let f(x) and g(x) be two real polynomials of degree 2 and 1...

Given, $f\left(g\left(x\right) = 8{x}^{2} - 2x\right)$and g\left(f\left(x\right) = 4{x}^{2} + 6x + 1\right)

Let $f\left(x\right) = c{x}^{2} + dx + e$ and $g\left(x\right) = ax + b$

So, $f\left(g\left(x\right)\right) = c{\left(ax + b\right)}^{2} + d\left(ax + b\right) + e = 8{x}^{2} - 2x$

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

On comparing both side we get, $a = 2, b = - 1, c = 2, d = 3, e = 1$

So, $g\left(x\right) = 2x - 1 ⇒ g\left(2\right) = 3$

$\text{ and } f\left(x\right) = 2{x}^{2} + 3x + 1$

$f\left(2\right) = 8 + 6 + 1 = 15$.

So, $f\left(2\right) + g\left(2\right) = 18$