Geometry Question

Let P be the point on the tangent at the bottom of the image.

Note that $\angle PXZ = \angle XZW$ since they are alternate angles of the pair of parallel lines.

Also, $\angle PXZ = \angle XWY$ since they are angles in alternate segments.

Therefore $\angle XZW = \angle XWY$. Also, $\angle ZXW = \angle WXY$ since they are the same angle.

By AA postulate, $\triangle XZW \sim \triangle XWY$.

Let YZ = t. Then by similar triangles, $\dfrac{XZ}{XW} = \dfrac{XW}{XY}$. i.e., $\dfrac{14 - t}{6} = \dfrac{6}{14}$.

Can you take it from here?