In simple Physics exercises, if you see mass and acceleration in the same Problem, think at once of the formula F = ma. Force = mass*acceleration.
What is the force that will move the crate for any acceleration?
Why, F = (20 kg)*a = 20a newtons, of course?
What will prevent the crate from moving?
Force due to friction = (0.400)(20kg *(9.8newtons /1 kg) = 78.4 newtons.
So if F = 20a is to overcome the 78.4 N friction force, to move the crate, then
20a > 78.4
a > 78.4 /20
a > 3.92 m/sec/sec
Therefore, the flatbed can accelerate to a maximum of 3.92 m/sec/sec before the crate starts moving. -------------answer.