Almost everyone would have encountered left/right handed systems in their physics class at high school. But can easily get mixed up and confuse the axes when the need arises. If you follow this simple rule you will always end up with the correct answer.

Rule

Axes are fixed to the fingers. You cannot switch them.
$$\color{red}{Thumb\ finger\ -\ X\ axis}$$ $$\color{green}{Index\ finger\ -\ Y\ axis}$$ $$\color{blue}{Middle\ finger\ -\ Z\ axis}$$

Tip

Generally the colors red, green and blue (RGB) are assigned to the X, Y and Z axes respectively. Though it is not a rule, it is a convention and if you stick to it, it makes life a lot easier. The famous Robot Operating System (ROS) also follows this convention.