An object experiences a net force and accelerates from rest to its...

When the mass increases by a factor of 4 the acceleration must decrease by a factor of four if the same force is applied. The question asks about position so we need to relate acceleration and time to position. We can do this by the equation $: x_{f}-x_{i}=v_{x i} t+1 / 2 a_{x} t^{2}$ We want the change in position to stay the same. The initial velocity is zero so in order for the change in position to remain constant the term $(1 / 2)$ at ^{2}$must remain the same. If the acceleration is reduced by a factor of 4 you can see that the time must be increased by a factor of 2 in order for the term to remain the same.$