Matrices and Multiplication

I am reading the NeHe tutorial in Vectors and Matrices. In 7th grade, my math teacher there is no way to multiply matrices with diff. columns and rows. I found different on the tutorial. Can someone explain exactly how to do this?

In the tutorial:

| 1 3 | | 1 3 5 |

M = | 2 4 | X = | 2 4 6 |

M*X= | 7 15 23 |

| 10 22 34 |

The tutorial says:

Now, lets get on with doing the actual matrix multiplication! To do this, you multiply each row of the first matrix by

each column of the second matrix.

Can anyone explain how to get M*X?