Voltage across and current through the LED load
Figure 1. A white LED I-V curve showing a nominal value and possible spread in values from device to device. Source: LED binning.

The forward voltage, VF, drop across an LED remains fairly constant over a range of current values. In your case we can assume that it is 3 V in the region of interest. Let's check ...







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 2. The test circuit.

With 300 Ω in series on a 9 V supply there will be 6 V across the resistor. \$ I = \frac {V}{R} = \frac {6}{300} = 20 \ \text {mA} \$.

At 12 V supply there will be 9 V across the resistor so current will be up by 50% to 30 mA.

Looking at Figure 1 we can see that the voltage drop across the LED will not change significantly between 20 and 30 mA.