Given that triangle PQR is similar to triangle PWY, with WY parallel to QR, WY = 6 cm, QR = 15 cm, and WP = 4 cm, find the length of WQ.

We are given that $\triangle PQR$ is similar to $\triangle PWY$.
We are also given the lengths of the parallel sides: $|WY| = 6$ cm and $|QR| = 15$ cm.
The length of a segment on one side is given: $|WP| = 4$ cm.
We need to find the length of $|WQ|$.

Since $\triangle PQR \sim \triangle PWY$, the ratio of their corresponding sides is equal.
The side $WY$ in $\triangle PWY$ corresponds to the side $QR$ in $\triangle PQR$.
The side $PW$ in $\triangle PWY$ corresponds to the side $PQ$ in $\triangle PQR$.

The ratio of similarity $k$ can be found using the lengths of $WY$ and $QR$:

Now, we apply this ratio to the sides $PW$ and $PQ$:

Substitute the known values:

To solve for $|PQ|$, cross-multiply:

From the diagram, the segment $PQ$ is composed of two parts, $PW$ and $WQ$.
So, $|PQ| = |PW| + |WQ|$.
We know $|PQ| = 10$ cm and $|WP| = 4$ cm.

Subtract 4 cm from both sides to find $|WQ|$:

The length of $WQ$ is $\boxed{\text{6 cm}}$.