Work = Force x Displacement
The force must be in the direction of the displacement or motion in order to do work. We can calculate the component of force in the direction of displacement using F = W/d,
F = 300 J/20 m
1 Joule = 1 N-m, so F = 15 N
There are two other factors at play here. One is that if the handles of the wheel barrow are such that the force applied to move wheel barrow is exerted at an angle to the direction of displacement, then the actual applied force would be greater than the component calculated. You would need to know the angle at which the force is applied in order to calculate it.
The other factor is that the handles of a wheel barrow acts as a lever, decreasing the input force required to lift the legs off the ground.
So the calculated value of 15 N is the output force and not the input force.