How can transverse waves be produced on a rope?
You can produce transverse waves on a rope by moving one end of the rope up and down.
You create a transverse wave by inducing in the particles that make up a respective medium a motion perpendicular to the direction of propagation.
In your case, the medium will be the rope. When you move the rope up and down, you create motion in the particles that make up that rope.
This motion will create high points called crests and low points called troughs.
The particles themselves will only move perpendicular to the direction of propagation, but the wave itself, i.e. the crests and the troughs, will move along the direction of propagation.
Check out this great transverse wave simulator, you can play around with the type of movement you induce in the rope (the simulator is at the bottom of the page)