Powerplay Commodities are available from the Powerplay Contact in any Stronghold system.
(For Acquisition only, or also the Powerplay Contact in a Fortified system, and it needs to be a system in range of the Acquisition target)
For the system in your screenshot you will specifically need to pick up the supplies from the Wababaye system.
(Make sure you pick up the Acquisition commodity - there are three different types and only one of them works here: you want the "Aisling Media Material", though the other two probably won't be available in this case)
The main way to get them is from the various Power Signal Sources (scan the nav beacon, then return to supercruise and check your navigation panel).
You don't technicallly need to be good at combat to get them from there, but you probably do want a ship which can take a bit of a beating while your collector limpets do their job before you run away again.
This depends on
how you go about taking over the system - there are quite a range of possible Acquisition activities, some of which will make you popular with the factions in the system (bounty hunting, profitable trade sales, mining) ... some of which are neutral (use of Powerplay commodities, killing rival Power ships) ... and some of which will make you unpopular (holoscreen hacking, raiding Odyssey settlements for Powerplay goods and data).
Note that there are more Acquisition methods available than the ones listed in your screenshot (see the Pilots' Handbook in-game or
this post out of it) - the ones in the screenshot are just the ones you get bonus merits for.
Acquisition methods are also very picky about location: to keep things simple for this case, if anything requires transporting between systems, always transport it between the Wababaye system and the Col 285 Sector DR-N a36-2 system.