a glider with a mass of 5 kg is moving to the right on a horizontal frictionless surface at 6 m/s when it collides with a 8 kg glider that is at rest. After the collision, the 8kg glider is moving to the right at 6 m/s. what are the speed and direction of the 5 kg glider ?

Answer 1

before collision the light glider has kinetic energy of
(1/2)5(36)

there is no way the final kinetic energy of the system can be more than that

but you say
the heavy glider has speed 6 AFTER collision
(1/2)8(36)

That is impossible so there is no point in doing the conservation of momentum thing, which is also impossible.
You have a major typo I think.

Answer 2

Given:
M1 = 5kg, V1 = 6 m/s.
M2 = 8kg, V2 = 0.
V3 = Velocity of M1 after the collision.
V4 = 6 m/s. = Velocity of M2(8kg) after the collision.

M1*V1 + M2*V2 = M1*V3 + M2*V4.
5*6 + 8*0 = 5*V3 + 8*6,
5*V3 = -18,
V3 = -3.6 m/s(Left) = Velocity of M1(5kg) after the collision.