What minimum force f$,$ applied horizontally to the wheel axis, is needed to bring the wheel up to the height step h$?$

Tomer as the wheel radius and w as its weight.

Tip: apply the equilibrium conditions: sum of forces and sum of torques equal to zero, just at the moment when the wheel leaves the floor. At that moment the normal becomes zero. The axis of rotation, with respect to which the torques will be calculated, is the corner of the step.