Ultimately, your goal is to be able to listen to a piece of music and audiate its rhythm. That is to say, when you listen to a piece of unfamiliar music, your ears should tell you:

The aforementioned skills are indeed the goal, but are decidedly inference skills that come with much practice. We are now going to practice distinguishing between duple and triple meters using familiar patterns. This will give you the opportunity to learn how to distinguish between duple and triple meters with familiar or unfamiliar music. This skill is called Partial Synthesis. 

Watch the video lesson below. 

Then, try the Duple vs. Triple test to see how you do. If you get 7/10 or better, you're doing fine! If you score lower than that, you may wish to take a step back and work through the previous lessons again.