Answer:
None of the above
Step-by-step explanation:
The restaurant obliged new customers by refusing to take their reservations. - Obliged means to do something in order to please someone else. Refusing to take a customer's reservation would not be pleasing.
The sun's gravity causes the earth to revolutionize around it. - Revolutionize means to change greatly, like the discovery of nuclear reactors revolutionized the way humans produce clean energy. The correct word to use would be revolve. Revolve means to move around in a circular fashion, which is the motion with which celestial bodies move about the sun.
Some people think my friends are eccentric because they enjoy popular television shows. - Eccentric means strange or unconventional. Popular TV shows are the opposite of what an eccentric one would watch. If popular was replaced with "unpopular", this sentence would be correct.
The homely garden was filled with dead branches, wilted flowers, and rotting fruit. - The word "homely" describes either an unattractive PERSON, or something that is cozy like one's home. The first definition is contradictory because a garden is not a person. The second definition is does not fit this sentence because the items in the garden would render it the opposite of cozy and comfortable.