The pulley arrangements of Figs. (a) and (b) are identical. The mass of the rope is negligible. In (a) the mass m is lifted up by attaching a mass 2m to the other end of the rope. In (b), m is lifted up by pulling the other end of the rope with a constant downward force `F=2mg`. The acceleration of m is the same in both cases

Explanation

In case (A) the pulling force `=2mg-mg=mg` and the mass is
`2m+m=3m`
So, accleration `a=(mg//3m)=g//3`
While in case (B), the pulling force `=2mg-mg=mg`
but he mass in motion `=m+0=m`
So, acceleration `a' = (mg//m)=g`
i.e, acceleration in case (B) is more (actually 3 times) than in case (A).