3. D.
$F(x)-2=a f(x)+b g(x)$ is an odd function, $F(x)-2$ has a maximum value of $8-2=6$ on $(0,+\infty)$, so $F(x)-2$ has a minimum value of -6 on $(-\infty, 0)$, thus $F(x)$ has a minimum value of -4 on $(-\infty, 0)$.
3. If $f(x)$ and $g(x)$ are both odd functions, and $F(x)=a f(x)+b g(x)+2$, has a maximum value of 8 on $(0$, $+\infty)$, then on $(-\infty, 0)$, $F(x)$ has $(\quad)$.
A. Minimum value -8
B. Maximum value -8
C. Minimum value -6
D. Minimum value -4