In the arrangement shown in the figure, the acceleration of the pulley is, (Ignore friction)

Equating the forces acting on the pulley

2T=F $\Rightarrow$T=F/2

Forces acting on the block are T

So T=ma$\Rightarrow$a=F/2M

From constraint equations acceleration of pulley=1/2 x acceleration of block

So the acceleration of pulley=F/4M