Find the current through the 16 k resistor.

To find the current through the 16 k resistor, we first need to determine the total resistance in the circuit.

Given that the circuit consists of a 12 V battery, a 4 k resistor, a 8 k resistor, and a 16 k resistor in series, the total resistance can be calculated as follows:

Total resistance = 4 k + 8 k + 16 k
Total resistance = 28 k

Next, we can use Ohm's Law to calculate the current through the circuit:

I = V / R
I = 12 V / 28 k
I = 0.4286 mA

Therefore, the current through the 16 k resistor is 0.4286 mA.

Using Kirchhoff's voltage law, we can write:

```
-9 V + 16 k - I + 4 k - I = 0
```

Solving for I, we get:

```
I = 9 V / (16 k + 4 k) = 0.45 mA
```

Therefore, the current through the 16 k resistor is 0.45 mA.