From my experience, many students struggle with SN1, SN2, E1, and E2 reactions. It isn't that they should, but this problem exemplifies how or why it might be difficult. I also confess that I was a synthetic organic chemist so the objective of performing any reaction was to obtain a product in as high a yield as possible. It was counter to my purpose to run a reaction in which the mechanism to be performed should be unknown or questionable.
It occurs to me that the hand out was written in that manner. However, the clue does sensibly resolve this problem. That is, solve each problem sequentially. What are the possible SN1 products? Repeat with E1, SN2, and E2 elimination.
My rational for saying that is while it is possible to perform a reaction in which SN1 and SN2 reactions will compete with each other, generally you will chose one or the other. That is, if you wished to perform an SN2 reaction, you should use an SN2 solvent with high concentrations of nucleophile and halide. While an E2 elimination can and in this case will result in the major product, you would not expect to find the SN1 and E1 elimination reactions to any great extent (if at all). Similarly, if the sodium methoxide concentration is very low, then SN1 and E1 mechanisms will predominate and give a different spectrum of products.