The correct answer is B. Extract.
To elicit something is to draw it out or bring it forth. It can be used in a variety of contexts, such as eliciting a response from someone, eliciting information, or eliciting a reaction.
Induce means to cause something to happen or to bring about a particular state of mind. It can be used in a variety of contexts, such as inducing someone to do something, inducing a reaction, or inducing a change in behavior.
Divulge means to make something known or to reveal a secret. It can be used in a variety of contexts, such as divulging information, divulging a secret, or divulging a plan.
Instil means to put something into someone’s mind or to cause someone to develop a particular attitude or feeling. It can be used in a variety of contexts, such as instilling confidence, instilling fear, or instilling hope.
In this case, the best synonym for elicit is extract. This is because extract means to draw something out or to bring it forth, which is exactly what elicit means. The other options do not accurately reflect the meaning of elicit.