Two 20 newton forces act concurrently on an object what angle between these forces produce a resultant force with the greatest magnitude

Let θ₁ and θ₂ be the angles between the two forces and the direction of motion.

To produce motion in the indicated direction, the net force is
F = 20 cos θ₁ + 20 cos θ₂
   = 20 (cos θ₁ + cos θ₂)
   = 40 cos [(θ₁+θ₂)/2] cos[(θ₁-θ₂)/2]

The maximum value of the cosine function is 1, and it occurs when its argument is zero.
Therefore the maximum value of F occurs when
θ₁ + θ₂ = 0
or
θ₁ - θ₂ = 0

Add the two equations to obtain 
2 θ₁ = 0  => θ₁ = 0
Also,  θ₂ = θ₁ = 0

The angle between the two forces is zero.