Help me understand my membrane potential assignment
If there is passive transport for each ion, then every ion will diffuse over the membrane until the concentrations will be the same, and the membrane potential will be zero. So there is active transport in the cell, which maintains the resting potential which is -63mV.

So with the current concentrations the membrane potential will differ from this -63mV, and so the cell will change the ion levels to change the current potential to be equal to the resting potential.

I think you should try to simply summarize the Nernst potentials. It won't be so accurate as the Goldman equation, but you don't have the relative permeabilities of this cell type, so the questioner probably does not wait the Goldman equation from you.

I would solve it this way:

Em = RT/zF * ln(out/in)

R = 8,314 J/molK
T = 37 + 273 = 310K
F = 96485 J/molV

RT/F = 26,712mV

ENa = 26,712mV*ln(136/45) = +29,543mV
EK = 26,712mV*ln(6/100) = -75,152mV
ECl = -26,712mV*ln(140/13) = -63,486mV
Em = ENa + EK + ECl = -109,95mV

Emr = -63mV
Emr - Em = -63mV + 110mV = +47mV


So we have to increase the membrane potential. Decreasing intracellular K+, Cl- concentration and increasing intracellular Na+ concentration can do that.

Concentrations: extracellular 136 Na, 6 K, 140 Cl, intracellular 45 Na, 100 K, 13 Cl. So possible passive transports are increase Na+, decrease K+, increase Cl-.

Conclusion the passive transports will be increasing Na+, decreasing K+ the active transport will be decreasing Cl-.

Note that I haven't used these terms for 5 years, so if you can consult with somebody else about this, then ask him/her whether this is correct.