If a + 3b = 12 and ab = 9, then the value of (a - 3b) is:

Given, $$a+3b=13$$

$$\Rightarrow$$  $$\left(a+3b\right)^2=12^2$$

$$\Rightarrow$$  $$a^2+9b^2+6ab=144$$

$$\Rightarrow$$  $$a^2+9b^2+6\left(9\right)=144$$

$$\Rightarrow$$  $$a^2+9b^2+54-6ab+6ab=144$$

$$\Rightarrow$$  $$a^2+9b^2-6ab+6ab=90$$

$$\Rightarrow$$  $$\left(a-3b\right)^2+6ab=90$$

$$\Rightarrow$$  $$\left(a-3b\right)^2+6\left(9\right)=90$$

$$\Rightarrow$$  $$\left(a-3b\right)^2+54=90$$

$$\Rightarrow$$  $$\left(a-3b\right)^2=36$$

$$\Rightarrow$$  $$a-3b=6$$

Hence, the correct answer is Option C