What is a cross product?
A cross product is an operation done on two vectors that returns the vector that is perpendicular to both of them. Interestingly, the magnitude of a x b = ||a|| * ||b|| * sin(theta), which is also the area of the parallelogram created by the two vectors.
Right Hand Rule
The right hand rule is a rule that says that the cross product goes from the right vector to the left vector. So you could make this with your hand.
Basically b x a = -(a x b).
How to do it
3x3 Matrix Determinant
Here's a really good video about it.