To rationalize the denominator of the expression $\frac{6}{3\sqrt{2}}$, we need to eliminate the square root from the denominator. This can be accomplished by multiplying both the numerator and the denominator by $\sqrt{2}$.

Rationalizing the denominator is the process of converting a fraction so that the denominator is a rational number, meaning it contains no square roots. Starting with the expression $\frac{6}{3\sqrt{2}}$, we can achieve this by multiplying both parts of the fraction by $\sqrt{2}$. This is effective because the product of $\sqrt{2}$ and itself yields a rational number:

$\sqrt{2} \times \sqrt{2} = 2.$

Let’s perform the multiplication:

$\frac{6}{3\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{6\sqrt{2}}{3\sqrt{2} \times \sqrt{2}}.$

Next, we simplify the denominator:

$3\sqrt{2} \times \sqrt{2} = 3 \times 2 = 6.$

Now, substituting this back into our expression gives:

$\frac{6\sqrt{2}}{6}.$

At this point, we can further simplify the fraction by dividing both the numerator and the denominator by $6$:

$\frac{6\sqrt{2}}{6} = \sqrt{2}.$

Thus, the rationalized form of $\frac{6}{3\sqrt{2}}$ is:

$\sqrt{2}.$