Psychology has always walked a dangerous line between being a natural science and a social science. A natural science, of course, deals in the natural world. Examples would be physics, chemistry, or earth sciences. A natural science is rooted in numbers and hard facts. A social science, on the other hand, examines the human condition. The trouble with that is that humans are not always mathematical. Things like thoughts, feelings, and emotions can make psychology, frankly, a bit messy when it comes to facts. Think of psychology as walking a tightrope between the two brands of science. We are attempting to better understand someone's thoughts, beliefs, and emotions through the scientific and experimental methods.
When it comes to your personal experiences with these big ideas, you will need to add in your own actual personal experiences. However, I will provide definitions and some possible examples for each to get you thinking.
Critical thinking is the process of examining something with objectivity. The goal is to form an informed opinion of something. So your example may be something from your own life that dealt with you having to make the best decision based on the available evidence at that time. The biopsychosocial approach is exactly what it sounds like. You use elements of biology, psychoanalytics, and sociology to examine someone's behavior. This is a more eclectic approach to psychology. Your example could be something like a situation in which only one approach doesn't get you the answer that you are seeking. The dual processing theory gives us the notion that human thought can arrive from multiple locations. This is where your lessons on Freud and the unconscious mind come home to roost. An example might be a Freudian slip or slip of the tongue. Someone is trying to consciously say one thing, but their unconscious mind interjects something else into the conversation. Hence, thought from two different locations.
And lastly, explaining human strength can mean several things. However, your instructor is most likely referring to positive psychology. In positive psychology, the six human strengths are wisdom, courage, humanity, justice, temperance, and transcendence. Each of these refers to a character trait that each of us possess to one degree or another. So for your example on this point, you would want to draw from your own personal life and possibly judge yourself on how much of these character traits you exhibit in your daily life.