Identify the angles in PQT.

We are given that $\angle PTR = 90^\circ$, which means $\triangle PQT$ is a right-angled triangle at $T$.
We are given $\angle PQR = 30^\circ$.
The sum of angles in $\triangle PQT$ is $180^\circ$.
So, $\angle QPT = 180^\circ - \angle PTQ - \angle PQT = 180^\circ - 90^\circ - 30^\circ = 60^\circ$.

We know $|PQ| = 6\sqrt{3} \text{ cm}$ and $\angle PQT = 30^\circ$.
In $\triangle PQT$, $|PT|$ is the side opposite to $\angle PQT$, and $|PQ|$ is the hypotenuse.
We use the sine function:

We know that $\sin(30^\circ) = \frac{1}{2}$.

We know that $\triangle PRT$ is a right-angled triangle at $T$.
We are given $\angle PRT = 60^\circ$.
We found $|PT| = 3\sqrt{3} \text{ cm}$.
In $\triangle PRT$, $|PT|$ is the side opposite to $\angle PRT$, and $|RT|$ is the side adjacent to $\angle PRT$.
We use the tangent function:

We know that $\tan(60^\circ) = \sqrt{3}$.

Now, solve for $|RT|$:

Comparing this with the given options, the correct option is C.

The final answer is $\boxed{\text{C. } 3\text{cm}}$.