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With what acceleration a should the box ...

With what acceleration a should the box of figure descends so that the block of mass M exerts a force Mg/4 on the floor of the box?

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The block is at rest with respect to the box which is accelerating with respect to the ground. So, the acceleration of the block w.r.t. the ground is .a. downward. The forces on the block are as follows:
i) Weight Mg downward (exerted by the earth)
ii) Normal reaction R upward (exerted by the floor)
Equation of motion of block is:
`Mg- R = Ma , " But " R=(Mg)/(4)`
`:. Mg-(Mg)/(4) =Ma or (3Mg)/(4) =Ma implies a=(3g)/(4)`
The block and hence the box should descend with an acceleration 3g/4.
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