There are many uses of the expression/gesture.
"Throwin' your sixes up" can be considered similar to the middle finger, but slightly less offensive.
It is typically used by and individual to show that they thing something is wicked or sick.
Also, it can be used by an individual to show that they don't care about something.
The origin "throwin' your sixes up" is associated with the number 666.
"Some lady cut me off and I just threw my sixes up at her"
"That party was awesome, all the kids were just throwin their sixes up"
"Why weren't you throwin' your sixes up? That lady's a bitch"