The two spheres start at a seperation of 12R, and end at a seperation of 4R,
so the change in potential energy of the system is equal to the work required
to take the spheres from a seperation of 4R to one of 12R:
DE=int(r=4R:12R) G _1 m_2/r^2 dr = G m_1 m_2/(6R)
So as the spheres start from rest this is equal to the sum of their KE's
when they hit:
G m_1 m_2/(6R) = (m_1 v_1^2 + m_2 v_2^2)/2.
The conservation of momentum gives:
m_1 v_1 = -m_2 v_2.
Solve these two equations to find v_1 and v_2.