Answer
We assume the probe's motion to be in positive direction.
The probe's momentum after the retrorocket ceases to fire is $+5.1\times10^7kg.m/s$
Work Step by Step
We assume the probe's motion to be in positive direction.
According to the impulse-momentum theorem, $$\sum\vec{\overline F}\Delta t=\vec{p}_f-\vec{p}_0$$ $$\vec{p}_f=\sum\vec{\overline F}\Delta t+\vec{p}_0$$
The probe's initial momentum (same direction as the probe's motion) is$\vec{p_0}=+7.5\times10^7kg.m/s$, and the only force (opposing the probe's motion) is $\vec{F}=-2\times10^6N$ for $\Delta t=12s$
The probe's momentum after the retrorocket ceases to fire is $$\vec{p}_f=+5.1\times10^7kg.m/s$$
