Two small objects each with a net charge of +q exert a force of magnitude f on each other: we replace one of the objects with another whose net charge is +4q: the original magnitude of the force on the +q charge was f; what is the magnitude of the force on the +q charge now?

The force between 2 charged objects is given by, F = kq1q2/d².
where k ⇒ constant
          d ⇒ distant between the 2 objects.
 
In this case, k and d are constants.
So, let k/d² = x
since q1=q2,
F = xq²
x = F/q²
After replacing q1  with 4q, the new force on +q will be:

F = xq.4q
    = Fq4q/q²
    = 4F

The new charge on +q is 4F.