Find four current mesh
It's not clear from the wording of the question whether you are being asked to transform the mesh into one having four current sources, or, as is more likely, I think, you are being asked to perform a mesh (current-loop) analysis. 

That is, analyze the circuit by using the current-loop procedure sketched here:



If this is right, then proceed to write equations:


KCL for nodes A, B, C, G, in terms of IL1..4), 
Voltage equations for nodes A, B, C relative to G, again in terms of IL1..4 (you can call VG = 0)
Equations that relate ILs to known currents (examples: IL4 = -I2, I1 = IL2 - IL3)


Be sure to keep the voltage and current signs correct relative to loop-current current direction. (Example, For the voltage across R5, IL3 contributes positively to VC, whereas IL4 contributes negatively.)

At that point you should have enough equations to be able to substitute and solve.