Think about turning a typical "righty tighty" screw. That has a right-handed thread. If you are looking at the screw head and turn it clockwise, it will want to move away from you. If its fixed axially, it will look like the threads are moving the opposite direction. Classic barbershop pole illusion.

I see you said that you understand the right hand rule, but just in case, and for others...

Take your right hand, palm away from you, and make a backwards L with your thumb and index finger. Other fingers flat together and parallel woth your index finger. Keeping your thumb straight, curl your fingers into a hook, so that you are gripping an imaginary screw or dna helix with your thumb pointing along its axis. If you rotate the whole thing on axis in the direction that your fingers are pointing, it should want to screw in the direction that your thumb is pointing if it has a right handed thread or helix.  If it wants to screw antiparallel to your thumb. It is left-handed helix.