If the average income of American consumers falls, we would expect to see: a

The answer is a.

With a lower income, American consumers will purchase less of a given good at any given price. Therefore, the demand curve shifts leftward.

Consider a more concrete example. Lobster price changes considerably through the year. When you have a job and hence an income, you consume 4 lobsters when they are cheap, and 2 lobsters when they are expensive. Now suppose you lost your job and your income is zero (i.e., reduced), you will consume zero lobster no matter what the price is. That is, your quantity demanded for lobster is lower at any given price. In this case, your demand curve for lobster is shifted to the left.