A person ran with a speed of 6 m/s onto the skateboard .What is the speed with which he ride on the skate board

Let's define:

M = mass of the person

m = mass of the skateboard.

We can write the momentum as:

P = M*v

Remember the conservation of momentum, as we can not find any force in this situation (a highly idealized situation) the momentum will be conserved.

if P is the momentum before the person rides the skateboard, P' will be the momentum after the person rides the skateboard.

P = M*v

P' = (m + M)*v'

We must have:

P = P'

Now, we can assume that the mass of the skateboard is a lot smaller than the mass of the person, such that:

m  << M

then we can assume:

(m +M) ≈ M

then:

P' = (M + m)*v' ≈ M*v'

And this is equal to P.

M*v' = M*v

Then we must have that:

v' = v

and we know that v = 6m/s

Then v' = 6m/s

The velocity after riding the skateboard will be equal to the velocity before riding it (in this model)

In a more scientific way, the velocity after riding the skateboard will be a bit smaller than the velocity before, and it will depend on the mass of the person and the mass of the skateboard.