Do not "stretch" yourself! It may not be realistic for you to solve various statistical problems even after completing an introductory course in statistics. In fact, it is already a blessing if you can solve a small portion because statistics is a huge subject area that can be broken down into many specializations. It may take years before one can develop a good statistical sense.
Nevertheless, when going through the course materials and exercises, you may aim to (i) be able to do the basic computations; (ii) get a sense of when to use the different methods; and (iii) be able to interpret basic statistical results. For example, when we discuss the mean, median and mode, you should also be able to tell their pros and cons. By doing the exercises, I hope you could suggest the most appropriate statistical approach in practice rather than being instructed what to use.