My group has an astrogation droid that they pick up in an earlier adventure ( we are using the standard card for the droid) recently they also put in an astrogation droid brain. Under Mod Options it say 2 Increase - Does that mean you can increase the skill twice for a total of 4 ( 2 original and then the 2 Increase)?

Skill question On astrogation difficulty of hard with 2 setback dice and using the droid brain with the R4 assisting does the dice pool look like this?

3 purple

2 black

4 green

and 1 blue from assist from the R4?

Yes, since it's base skill is 2, then if you succeed at both mods, it increases the skill by another 2 total, bringing it to 4 greens before any possible things that could upgrade it.

And yes, that would be dice roll, again, provided all mods were succeeded.