ELI5: Why does multiplying two negatives give you a positive?

I give you three $20 notes +3 * +20 = +60 for you
I give you three $20 debts +3 * -20 = -60 for you
I take three $20 notes from you -3 * +20 = -60 for you
I take three $20 debts from you -3 * -20 = +60 for you

and quick note - the result is the gain or loss from where you started.

ANOTHER GREAT EXPLANATION BELOW

Think about it like this: If you film someone running forwards
(positive) and then play the film forward (positive) he is still running
forward (positive).

If you play the film backward (negative) he appears
to be running backwards (negative) so the result of multiplying a
positive and a negative is negative.

Same goes for if you film a guy
running backwards (negative) and play it normally (positive) he appears
to be still running backwards (negative).

Now, if you film a guy running
backwards (negative) and play it backwards (negative) he appears to be
running forward (positive). Even if you speed up the rewind (-3x or -4x)
these results hold true. Backward x backward = forward. Negative times
negative = positive.

Explain Like I`m Five: good questions, best answers.