Ok so... I think i get this (sorry for being a noob, I just havent ran a RPG for ohh.... 10 years or so)
Re-rolling the character, once again a starship officer at Conn who has an INT of 12 so gets a +3 modPersonal Package (Starfleet Brat) : System Operation +1
Professional Package (Base Skills) : System Operation
Professional Package (Hot Shot Pilot) : System Operations (Flight Control) +4
Professional Package (5 picks) : System Operation + 1
The "Professional Package (Base Skills)" can be ignored, its just an indication this character gets the System Operations skill as a professional skil so we can ignore this and focus on the other areas beingINT Modifier +3
System Operation +1
System Operation (Flight Control) +4
System Operation +1
So written on the character sheet would be :-
System Operation (Flight Control) : AttMod+3 : Levels+6 : Misc+0 : Total+9
When the character makes a System Operation test he gets a bonus of +9, when the character makes a flight control test he gets a bonus of 9+2=+11 (for the speciality) and its pointless using any more of the 5 picks to boost the System Operation skill as it is cap'd at +6 (for a new character)