m1

Find by comparing change in momentum and using impulse formula ( I = mv-mu )
m1v1+m2v2=m1u1+m2u2

m1 - mass of particle a
m2 - mass of particle b
u1 - initial speed of a
u2 - initial speed of b
v1 - final speed of a
v2 - final speed of b

Sorry for the lack of detail

the part on the left is conservation of momentum.

B will have more momentum than A, so the particles will move in the initial direction of B. One Impulse is always negative, as there are equal and opposite forces acting on the particles when they collide.

oh so since values of B are bigger the final velocity of A should be going left?

so either the arrows point away from each other or towards each other? because they both exert an impulse on each other?

When a collision takes place, one object (A) will provide a force on the other object (B). The other object (B) will provide an equal and opposite force on the that object (A). No the arrows (velocity) could be both be point the same way before and after the collision. But the transfer of momentum (impulse will be in opposite directions).

so when it says impulse exerted on B by A that means that A provides the force so .... i'm still confused as to which direction the final velocity of A goes...

The direction is the direction which converse momentum. If B is on the right and moving right to left. And A is on the left moving left to right. A and B will collide . After the collision B is still moving Left, A has to now be moving left as A cannot go through B.