“Gregarious” refers to someone who enjoys being with others and is sociable. The other options (shy, solitary, reserved) are antonyms of gregarious.
“Ephemeral” describes something that lasts for a very short period of time. The other options (permanent, long-lasting, frequent) have the opposite meanings.
In this context, “obscure” means that the theory was not easily understood and was complex or difficult to grasp. The other options (simple, clear, obvious) would not fit the description of something that takes years to understand.
“Amiable” describes a friendly and pleasant manner, which fits well with being popular and approachable. The other options (hostile, aloof, aggressive) describe negative or distant attitudes.
“Elucidate” means to make something clear or to explain it. It is the opposite of confusing, ignoring, or obscuring, which involve making something less clear.