To "determine" something means to figure it out or make a decision about it. "Determine" is a formal word, so you can use it in situations like when describing legal decisions:
The judge determined that Medco was responsible for the patients' medical issues. They were required to pay a large settlement.
Or you can use it in a business setting:
Have they determined when the merger will take place?
After "determined", you can use a clause like in the previous examples, or a noun:
Once we've determined the cause of the outage, we'll send a full report.