The center of mass of a system of two particles of masses m1 and m2 is at the origin. If mass m1 is moved by a distance vec{d} towards the origin, by…

For the center of mass to remain unchanged, the total shift in position of the center of mass must be zero. That is, $m_1 \Delta \vec{r}_1 + m_2 \Delta \vec{r}_2 = 0$. Given $\Delta \vec{r}_1 = -\vec{d}$ (moving towards the origin), we have $m_1(-\vec{d}) + m_2(\Delta \vec{r}_2) = 0 \implies \Delta \vec{r}_2 = \frac{m_1}{m_2}\vec{d}$, which means $m_2$ must move away from the origin by this distance.