Let the retarding force exerted by one plank be F and displacement inside the plank be x.
So, using work energy theorem for one plank,
Work done = ΔKE of the bullet
−F.x=12m[(1920v)2−v2] ……(1)
Applying work energy theorem for n planks, −F.nx=12m[0−v2]…(2)
Using value of Fx from (1) in (2)
12m[(1920v)2−v2]n=12m[0−v2]
Solving, we get n=10.25
So, 11 planks are needed to just stop the bullet.