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?

Friction.

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.