The ACS is lists things the pilot should know, have adequate skill to perform and have an idea of the risks involved.
In fact, the ACS is separated into these three areas for each task involved.
The code you referenced is easy to figure out.
PA is private airplane ACS
IX is Emergency Procedures
C is Systems and Equipment Malfunctions
K1a is Engine roughness or overheat
The last section has a code of k, R or S
K is for knowledge areas
R is for risk areas
S is for skill areas
Listed under the task are the references for this task.
FAA-H-8083-2 - Risk Management Handbook
FAA-H-8083-3 - Airplane Flying Handbook
Airplane specific POH/AFM
The answer on how to deal with engine roughness will come from these references. After you acquire the theory, you will have more common sense on the correct procedure to follow.
In this specific case, if there is engine roughness I would turn on the carb heat and pull out the checklist. If there is no checklist, I would adjust the fuel mixture while contacting ATC and looking for an adequate airport to land at. I would inform the passengers of the situation and the need to possibly divert to a different airport. I would continually update my passengers with my plan of action as the situation continues.
I would think an answer from the examiner on why engine roughness would occur, how to possibly correct it and the decisions to be made on the flight afterwards would satisfy the ACS requirement.
The examiner will provide you a scenario during the oral and practical portions of the flight check. They are looking for you to make the best decision available for the scenario while maintaining safety of flight and flying with the regulations
To be best prepared for the oral and flight check, I would suggest you read all the reference material you can. Discuss different scenarios with your instructor both on the ground and in flight and just don't meet the minimum skill tolerances but be able to consistently fly with tighter tolerances.
