Look at the "6"
I think the easiest thing is to focus on 6s. Notice that the hitting hands are the one that contained 6s. But we still stand on 5-5-6. So here is a rule:
Hit if the hand has more 6s than 5s.
I believe this rule is specified in Griffin.
Note that this rule will misplay the 10-3-3 listed above. So it is not perfect.
Now knowing the fine points of BS is not that important for a card-counter. You would only use it in very limited circumstances: when this was the first hand and you could not see any others players cards, as when you are playing head-on.
But knowing the role of the 6 is very useful to a counter. When many 6s have been played, you can hit even in higher counts.