So we're going to start with the left most loop, and

we're going to use Kirchhoff's Voltage Law to write the loop equation for that loop.

So if we start, again, at the left lower corner of our circuit, and we work our

way around the circuit, the first thing we encounter is the dependent source.

So this is our first equation for that left loop.

And so, we end up encountering the negative polarity of

the 24 Volt independent source first, so it's a -24 Volts is

the first component of our loop equation.

Then as we continue to travel around this left most loop,

we encounter the resister R1, and we have a plus V R1 that has dropped the cross it.

We are hitting the positive polarity of that voltage drop across R1 first.

We continue around that left most loop and come down and we encounter resistor R4.

And it has a voltage drop across it, V R4,

with the positive polarity is the one we encounter first.

And continue down that center leg of our circuit, and

we encounter a -16 volts, continuing around to where we began.

And that is our equation for our loop, understanding that a loop