Kirchhoff's Rules:

1. Junction (current) rule: the algebraic sum of currents meeting at any junction is zero (conservation of charge) — currents flowing in are taken positive, currents flowing out negative.
2. Loop (voltage) rule: the algebraic sum of potential differences (including emfs and IR drops) around any closed loop in the circuit is zero (conservation of energy).

Method: assign unknown currents to each branch (including FC), apply the junction rule at each node and the loop rule to each independent loop, and solve the resulting simultaneous equations for the current through FC. (The specific resistor/emf values in this circuit were not fully legible in the extracted question — apply the method to the actual figure to get the numeric answer.)