jmc

We could solve the equation by noting that we must have $x+3=6$ or $x+3=-6$, so $x=3$ or $x=-9$. Or, we could be a little crafty and write the equation as $|x-(-3)|=6$, which tells us that $x$ is 6 away from $-3$ on the number line. This means that $x$ is $-9$ or 3. Either way, the positive difference between the solutions is $3-(-9)=\boxed{12}$.