How to calculate the temperature at which a reaction becomes spontaneous?
You have the right equation.  But the problem already gives you the temperature at which $\Delta G$ is 8.9 kJ. 

Assume that $\Delta H$ and $\Delta S$ are constant and do not vary with temperature.  $\Delta G$ still will though because of the $T$ in the $\Delta G = \Delta H - T\Delta S$ equation.

So plug in the values for $\Delta H$ and $\Delta S$, and also the $\Delta G$ value that you think represents the transition from spontaneous to non-spontaneous.  You should be able to take it from there.