Find an article in an area of interest to you that reports a correlation matrix or a covariance matrix. Propose a factor model that you believe is likely to underlie the correlation matrix. Your factor model should be based on your ideas about the variables, not on observed correlations. Explain your reasoning: Why do you think that particular factor structure is likely?
Now, obtain the demonstration version of Mplus and conduct an exploratory factor analysis. Comment: does the analysis fit your ideas?
Next, fit a confirmatory factor analysis that reflects you ideas. Comment on the model fit.