Many factors can cause demand to decrease (shift back). Suppose, for example, that a new study shows that eating beef is more harmful to health than previously believed. Such a report would almost certainly cause the demand curve for beef to shift back.
On the graph to the right, the initial equilibrium price of beef is and the initial equilibrium quantity is . As a result of changing attitudes about beef, due to the new findings, the demand curve shifts from D1 back to D2. This causes equilibrium quantity to fall to and equilibrium price to drop to.
In our hypothetical story, as a result of a study on beef, people's taste changed causing demand to shift back (decrease) which led to a reduction in both equilibrium price and quantity. In any market, if demand decreases (shifts back and to the left), price and quantity both fall.