Aman of mass 80kg stands next to a stationary ball of mass 4kg on a frictionless surface. he kicks the ball forward along the surface with a speed 15m/s. calculate the man’s recoil speed.

We cause conservation of momentum.  The initial momentum of the situation is zero, since momentum is given by p=mv.  Initially v of the ball and man are zero so the total momenta (the sum of the ball's and man's momenta) is zero.
Conservation of momentum means the vector sum of the final momenta must equal zero.  That is, they will be equal and opposite.  When the ball goes forward at 15m/s the momentum is p=(4kg)x(15m/s)=60kgm/s.
The man must have the same momentum, but in the opposite direction (negative).  We can find his speed by considering the magnitude of his velocity:


Checking our work we see that an 80kg man moving at 0.75m/s gives
(80kg)(0.75m/s)=60kgm/s, as expected.