How many transversals can you draw on any two given lines?

Infinite transversal lines can be drawn on any two lines.

Suppose, we have two parallel lines d and e. The lines can be extended on either side indefinitely. Hence, we can draw infinitely many transversals that cut the lines at two distinct points.
In the figure, we have 3 transversals. The number of transversals can increase up to infinity.

The number of transversals that can be drawn to two distinct lines are infinitely many.