sum the currents about each one of the nodes.

So, if we look at node one, we see that we have three currents flowing into node one.

We have the current flowing through the 6 kiloohm resistor right to left.

We have the current flowing up through the 12 kiloohm resistor.

We have the current flowing right to left through our dependent voltage source.

So if we were to write those currents and

add them up we would have a known current based on nodal voltages for

the 12 kiloohm resistor and for the 6 kiloohm resistor.

But we would have two entities, an additional unknown current for

the dependent voltage source.

So we'd have the current flowing up through the 12 kiloohm,

the current flowing downward through the 6 kiloohm and

the current flowing right to left through the voltage source.