Let $$f(x)$$ and $$g(x)$$ be two real polynomials of degree 2 and 1 respectively. If $$f(g(x)) = 8x^2 - 2x$$, and $$g(f(x)) = 4x^2 + 6x + 1$$, then the value of $$f(2) + g(2)$$ is ______.

We are given that $$f(x)$$ is degree 2, $$g(x)$$ is degree 1, $$f(g(x)) = 8x^2 - 2x$$, and $$g(f(x)) = 4x^2 + 6x + 1$$. Let $$f(x) = ax^2 + bx + c$$ and $$g(x) = px + q$$.

Substituting into $$f(g(x))$$ gives $$f(g(x)) = a(px+q)^2 + b(px+q) + c = ap^2x^2 + (2apq+bp)x + (aq^2+bq+c),$$ and comparing this with $$8x^2 - 2x + 0$$ yields the equations

$$ap^2 = 8 \quad (1),\quad 2apq + bp = -2 \quad (2),\quad aq^2 + bq + c = 0 \quad (3).$$

Similarly, substituting into $$g(f(x))$$ gives $$g(f(x)) = p(ax^2+bx+c) + q = pax^2 + pbx + (pc+q),$$ and comparing with $$4x^2 + 6x + 1$$ yields

$$pa = 4 \quad (4),\quad pb = 6 \quad (5),\quad pc + q = 1 \quad (6).$$

From (1) and (4) it follows that $$p = 2$$ and $$a = 2$$. Then (5) implies $$b = 3$$, substituting into (2) gives $$q = -1$$, and using (6) yields $$c = 1$$. One checks that (3) is satisfied since $$aq^2 + bq + c = 2(1) + 3(-1) + 1 = 0$$. Hence $$f(x) = 2x^2 + 3x + 1$$ and $$g(x) = 2x - 1$$.

Finally, evaluating at $$x=2$$ gives $$f(2) = 2(4) + 3(2) + 1 = 15$$ and $$g(2) = 2(2) - 1 = 3$$, so $$f(2) + g(2) = 18$$, and the answer is $$\mathbf{18}$$.