Help with using AnyDice

I'm using AnyDice:

http://anydice.com/

to compare dice combat. What I'd like to do is get a visual on 3d6 vs 2d6. Meaning an attacker rolls 3 dice against a defender rolling 2 dice. What's the probability distribution of them winning.

I'm weighting the probability of point values for each dice as such:

A {1,2,3} yields 0 points
{4,5} yields 1 point
{6} yields 2 points

For example: A 3d6 roll of [1,4,6] would yield 3 points total.

I can get the point probability of rolling various amounts of dice by doing:

loop N over {1..5} {
output [count {4,5,6,6} in Nd6]
}

That gives me the point probabilities of rolling 1 to 5 dice. Now what I'd like to do is see how to compare point probabilities against each other. So if playerA was to roll 3 dice and playerB was to roll 2 dice, what would be the point distribution. In a 3d6 vs 2d6 scenario, I'd expect a point distribution in the range of [-4..6].

I'd eventually like to get a visual of all combinations Nd6 vs Md6 where N and M can be 1 to 5 dice.

Thanks for any help and/or examples.