When human beings go from Earth to Mars will they intercept the planet as it comes from their right, or from the left.

They will intercept as it approaches from the right relative to the path from the Earth.

Viewed from above the planetary plane, all planets are rotating in a counter clockwise direction.

The trouble with that one is that the answer must vary with whether or not the ship is upside down in a medium where there is no way of determining it.

I’m not making myself clear. Visualize watching the planet approach from the left. What happens if you simply flip the ship on its back? How do you determine up from down between the planets?

Good point
Let’s establish that you are always oriented approximately along the direction of earth’s axis with your head at North and you are facing your trajectory

That’s better as a stipulation, and probably nails it. We must insist that we and the travelers are rigidly oriented and ignore such distractions as the ship they’re caged in for reference. Since we, the travelers and both planets are all in the same plane, let’s agree to view the approach from either above or below the scene. Mars is of course traveling clockwise, and whether or not we view the planet approaching our travelers from their left or right must depend on whether the curve of the trip falls within or without the planet’s orbital path. In other words, you can draw lines from the Earth to Mars that will pass on either side. The question is thus “what you wanna do when you get there?”

I wanna land on it

Yes.

I looked it up and the explanation is amazingly simple (once the math is done). A rocket launched at the right time, direction, and speed will coast to Mars and join its orbit of the sun.

See the first animated image here:
Jet Propulsion Laboratory – Let’s Go to Mars! Calculating Launch Windows

That’s for launching to an outer planet. To reach Venus, which is in a lower orbit, you launch in the opposite direction.

Thanks! I was thinking about @josie ‘s question in the shower and think there’s one that can be posed as the solution to directions as reference points.

If you think about it, you can orient the ship to make Mars appear from whichever direction you choose relative to the ship.