To accommodate positive and negative numbers we need two extended number lines, with their zeros at the same place
Then multiplication of two negative numbers will always give a positive result, following the same geometrical structure.
The start, where the multiplier begins at 1
Now the 1 connects with the multiplicand -3
The multiplier is now placed at -2
And the parallel line from -2 connects to the 6 on the target line
This is so geometrical, and there is no “funny business”. None of the “ought to be 6”. No stuff about the distributive law.
The only geometry needs the Pythagoras theorem, and this will be the next post.