A window washer pushes his brush up a vertical window at constant velocity by applying a force F as shown below. The brush weighs 12N and the coefficient of kinetic friction is 0.2. Find the magnitude of force F

Hint: since the brush moves at constant velocity the sum of forces acting on it must equal zero.

He pushes it up with a force of 12N, to cancel the force of gravity.

I think not - the OP mentioned friction. Without seeing the diagram it's impossible to answer.

True. The angle of the brush is not known. Call it a. Then,

F = 12N / (cos a - 0.2 sin a) provided tan a < 5. Otherwise, he cannot push the brush up.

P. S. a is the angle of the brush from the vertical.