I understand (or at least thought I did) :D Kirchhoff's rules. When I got to this circuit; however, I got a wee bit confused. The arrows indicate where I placed my three arbitrary currents. When writing equations for the two smaller loops (the ones on the left), I didn't know which current to use for the middle portion (in red). Should I add another current here?
I recommend that you use the branch current method to solve these kinds of problems: Assign each distinct branch its own current. (In this circuit, I see 6 branches.)
When does current change? A good way to think of current is as water flowing through a pipe. Think of the voltage source as a faucet pumping out water. So what would happen if you had a pipe that forked? The water would reach it and the water would split, a portion going one way and another portion going the other. A more mechanical way of thinking of it is. Current changes when you have elements in parallel. What is the definition of parallel? A loose definition is when two elements share start/end nodes. So if you label all your nodes {A,B,C,...} and then arbitrarily assign a current from node A to B, A to C, ... then you will get your answer.