Because bagels and cream cheese are often eaten together, they are complements

Please see the attached file.

a. We observe that both the equilibrium price of cream cheese and the equilibrium quantity of bagels have risen. What could be responsible for this pattern - a fall in the price of flour or a fall in the price of milk? Illustrate and explain your answer.

The reason behind this is the fall in the price of flour. Since flour is used in making bagels, a fall in the price of floor would make production of bagels cheaper, thereby people will consume more of bagels. Since bagels and cream cheese are complementary goods, the equilibrium price of cream cheese increases.
b. Suppose instead that the equilibrium price of cream cheese has risen but the equilibrium quantity of bagels has fallen. What could be responsible for this patterns- a rise in the price of flour or a rise in the price of milk? Illustrate and explain your answer.

The reason behind this is the rise in the price of milk. Since milk has become dearer, cream cheese becomes more expensive, so its equilibrium price increases. Now because bagels and cream cheese are complementary goods, since people are consuming lesser cream cheese owing to the price rise, the equilibrium quantity of bagels falls.