Stop using right hand rule, use LEFT FIST RULE. And remember, your thumb is always in your fist covered by your four fingers.
WHY: Why should we use left-fist rule?
The thumb is in the fist which is more lively to some situation. (More in HOW section)
I do not want to put down my pen when I am thinking and writing. (Sorry for the left-handed)
WHAT: What is the left-fist rule?
Raise your left hand with thumb in your palm
Point your rest four fingers to $x$ OR one of the radius direction
Find a way so that you could scroll your fingers to $y$ direction to form a fist OR along the spin direction
the direction of your thumb is $z$ direction
HOW: How to apply the left-fist rule?
X-Y-Z direction: point fingers to $x$, find a way scroll to $y$, your thumb in your fist is pointing at $z$
Cross Product $\vec{A} \times \vec{B}$: pointing four fingers to the direction of $\vec{A}$ with thumb in the palm, then curling four finger to the direction of $\vec{B}$, thumb in the fist is the direction of $\vec{A} \times \vec{B}$
Torque direction: point fingers to the radius $R$, scroll with the force direction $F$, your thumb in your fist is pointing at the torque direction.
Ampere’s Law
The given condition is a straight line of current/magnetic field: point your thumb in your fist to the line’s direction, the scrolling direction of your four fingers is the magnetic field/current direction.
The given condition is a loop of current/magnetic field: scroll your four fingers along the direction of the loop, the pointing direction of thumb is the direction of magnetic field/current.
Motion in the magnetic field: scroll from $v$(Motion of the positive electron, not current and negative electron!) to $B$(in the magnetic field), thumb is the direction of $F/I$