Conservation of momentum so the total initial momentum in the system is equal to the total final momentum in the system. You must remember that if an object is travelling in the negative direction, you must put a negative sign for the velocity.
mv + mv = mv
plug in all the numbers
(0.0323)(4.50) + (0.078)(-1.12) = (0.0323 + 0.078)Vf
multiply everything together
0.14535 - 0.08736 = 0.1103Vf
simplify
0.05799 = 0.1103Vf
isolate for vf
Vf = 0.5257m/s east
