Answer
$\overline{\vec{F_2}}$ acts for $9.6ms$
Work Step by Step
Since both forces produce the same impulse, we have $$\overline F_1\Delta t_1=\overline F_2\Delta t_2$$ $$\frac{\Delta t_2}{\Delta t_1}=\frac{\overline F_1}{\overline F_2}=3$$
We know $\Delta t_1=3.2ms$, so $\Delta t_2=3\times3.2=9.6ms$
