Initial charges: $+q$ and $-2q$, separated by $r$ — opposite signs, so initial force is attractive:

$$F=\frac{k(q)(2q)}{r^2}=\frac{2kq^2}{r^2}\ \ (\text{attractive})$$

When brought into contact, total charge redistributes equally between the two identical spheres:

$$q_{new}=\frac{q+(-2q)}{2}=-\frac{q}{2}\ \text{on each sphere}$$

After separation to the same distance $r$, both charges are equal and negative (same sign), so the force is now repulsive:

$$F' = \frac{k(q/2)(q/2)}{r^2}=\frac{kq^2}{4r^2}=\frac{F}{8}$$

(since $F=2kq^2/r^2 \Rightarrow kq^2/r^2=F/2$, so $F'=\frac{F/2}{4}=\frac{F}{8}$)

So the spheres will now repel each other with a force $F/8$.